The following values of n=am+b allow S(n) to be written as S(cm+d)+e where c<a:
2m, 4m, 4m+1, 4m+2, 6m, 6m+2, 6m+4, 8m, 8m+2, 8m+4, 8m+5, 10m, 10m+2, 10m+4, 10m+6, 10m+8, 12m, 12m+1, 12m+2, 12m+4, 12m+5, 12m+6, 12m+8, 12m+9, 12m+10, 14m, 14m+2, 14m+4, 14m+6, 14m+8, 14m+10, 14m+12, 16m, 16m+1, 16m+2, 16m+3, 16m+4, 16m+5, 16m+6, 16m+8, 16m+10, 16m+12, 16m+13, 18m, 18m+2, 18m+4, 18m+6, 18m+8, 18m+10, 18m+12, 18m+14, 18m+16, 20m, 20m+1, 20m+2, 20m+4, 20m+5, 20m+6, 20m+8, 20m+9, 20m+10, 20m+12, 20m+13, 20m+14, 20m+16, 20m+17, 20m+18, 22m, 22m+2, 22m+4, 22m+6, 22m+8, 22m+10, 22m+12, 22m+14, 22m+16, 22m+18, 22m+20, 24m, 24m+2, 24m+4, 24m+5, 24m+8, 24m+10, 24m+12, 24m+13, 24m+16, 24m+18, 24m+20, 24m+21, 26m, 26m+2, 26m+4, 26m+6, 26m+8, 26m+10, 26m+12, 26m+14, 26m+16, 26m+18, 26m+20, 26m+22, 26m+24, 28m, 28m+1, 28m+2, 28m+4, 28m+5, 28m+6, 28m+8, 28m+9, 28m+10, 28m+12, 28m+13, 28m+14, 28m+16, 28m+17, 28m+18, 28m+20, 28m+21, 28m+22, 28m+24, 28m+25, 28m+26, 30m, 30m+2, 30m+4, 30m+6, 30m+8, 30m+10, 30m+12, 30m+14, 30m+16, 30m+18, 30m+20, 30m+22, 30m+24, 30m+26, 30m+28, 32m, 32m+1, 32m+2, 32m+3, 32m+4, 32m+5, 32m+6, 32m+8, 32m+10, 32m+11, 32m+12, 32m+13, 32m+14, 32m+16, 32m+17, 32m+18, 32m+19, 32m+20, 32m+21, 32m+22, 32m+23, 32m+24, 32m+25, 32m+26, 32m+28, 32m+29, 34m, 34m+2, 34m+4, 34m+6, 34m+8, 34m+10, 34m+12, 34m+14, 34m+16, 34m+18, 34m+20, 34m+22, 34m+24, 34m+26, 34m+28, 34m+30, 34m+32, 36m, 36m+1, 36m+2, 36m+4, 36m+5, 36m+6, 36m+8, 36m+9, 36m+10, 36m+12, 36m+13, 36m+14, 36m+16, 36m+17, 36m+18, 36m+20, 36m+21, 36m+22, 36m+24, 36m+25, 36m+26, 36m+28, 36m+29, 36m+30, 36m+32, 36m+33, 36m+34, 38m, 38m+2, 38m+4, 38m+6, 38m+8, 38m+10, 38m+12, 38m+14, 38m+16, 38m+18, 38m+20, 38m+22, 38m+24, 38m+26, 38m+28, 38m+30, 38m+32, 38m+34, 38m+36, 40m, 40m+2, 40m+4, 40m+5, 40m+8, 40m+10, 40m+12, 40m+13, 40m+16, 40m+18, 40m+20, 40m+21, 40m+24, 40m+26, 40m+28, 40m+29, 40m+32, 40m+34, 40m+36, 40m+37, 42m, 42m+2, 42m+4, 42m+6, 42m+8, 42m+10, 42m+12, 42m+14, 42m+16, 42m+18, 42m+20, 42m+22, 42m+24, 42m+26, 42m+28, 42m+30, 42m+32, 42m+34, 42m+36, 42m+38, 42m+40, 44m, 44m+1, 44m+2, 44m+4, 44m+5, 44m+6, 44m+8, 44m+9, 44m+10, 44m+12, 44m+13, 44m+14, 44m+16, 44m+17, 44m+18, 44m+20, 44m+21, 44m+22, 44m+24, 44m+25, 44m+26, 44m+28, 44m+29, 44m+30, 44m+32, 44m+33, 44m+34, 44m+36, 44m+37, 44m+38, 44m+40, 44m+41, 44m+42, 46m, 46m+2, 46m+4, 46m+6, 46m+8, 46m+10, 46m+12, 46m+14, 46m+16, 46m+18, 46m+20, 46m+22, 46m+24, 46m+26, 46m+28, 46m+30, 46m+32, 46m+34, 46m+36, 46m+38, 46m+40, 46m+42, 46m+44, 48m, 48m+1, 48m+2, 48m+3, 48m+4, 48m+5, 48m+6, 48m+8, 48m+10, 48m+12, 48m+13, 48m+16, 48m+17, 48m+18, 48m+19, 48m+20, 48m+21, 48m+22, 48m+24, 48m+26, 48m+28, 48m+29, 48m+32, 48m+33, 48m+34, 48m+35, 48m+36, 48m+37, 48m+38, 48m+40, 48m+42, 48m+44, 48m+45, 50m, 50m+2, 50m+4, 50m+6, 50m+8, 50m+10, 50m+12, 50m+14, 50m+16, 50m+18, 50m+20, 50m+22, 50m+24, 50m+26, 50m+28, 50m+30, 50m+32, 50m+34, 50m+36, 50m+38, 50m+40, 50m+42, 50m+44, 50m+46, 50m+48, 52m, 52m+1, 52m+2, 52m+4, 52m+5, 52m+6, 52m+8, 52m+9, 52m+10, 52m+12, 52m+13, 52m+14, 52m+16, 52m+17, 52m+18, 52m+20, 52m+21, 52m+22, 52m+24, 52m+25, 52m+26, 52m+28, 52m+29, 52m+30, 52m+32, 52m+33, 52m+34, 52m+36, 52m+37, 52m+38, 52m+40, 52m+41, 52m+42, 52m+44, 52m+45, 52m+46, 52m+48, 52m+49, 52m+50, 54m, 54m+2, 54m+4, 54m+6, 54m+8, 54m+10, 54m+12, 54m+14, 54m+16, 54m+18, 54m+20, 54m+22, 54m+24, 54m+26, 54m+28, 54m+30, 54m+32, 54m+34, 54m+36, 54m+38, 54m+40, 54m+42, 54m+44, 54m+46, 54m+48, 54m+50, 54m+52, 56m, 56m+2, 56m+4, 56m+5, 56m+8, 56m+10, 56m+12, 56m+13, 56m+16, 56m+18, 56m+20, 56m+21, 56m+24, 56m+26, 56m+28, 56m+29, 56m+32, 56m+34, 56m+36, 56m+37, 56m+40, 56m+42, 56m+44, 56m+45, 56m+48, 56m+50, 56m+52, 56m+53, 58m, 58m+2, 58m+4, 58m+6, 58m+8, 58m+10, 58m+12, 58m+14, 58m+16, 58m+18, 58m+20, 58m+22, 58m+24, 58m+26, 58m+28, 58m+30, 58m+32, 58m+34, 58m+36, 58m+38, 58m+40, 58m+42, 58m+44, 58m+46, 58m+48, 58m+50, 58m+52, 58m+54, 58m+56, 60m, 60m+1, 60m+2, 60m+4, 60m+5, 60m+6, 60m+8, 60m+9, 60m+10, 60m+12, 60m+13, 60m+14, 60m+16, 60m+17, 60m+18, 60m+20, 60m+21, 60m+22, 60m+24, 60m+25, 60m+26, 60m+28, 60m+29, 60m+30, 60m+32, 60m+33, 60m+34, 60m+36, 60m+37, 60m+38, 60m+40, 60m+41, 60m+42, 60m+44, 60m+45, 60m+46, 60m+48, 60m+49, 60m+50, 60m+52, 60m+53, 60m+54, 60m+56, 60m+57, 60m+58, 62m, 62m+2, 62m+4, 62m+6, 62m+8, 62m+10, 62m+12, 62m+14, 62m+16, 62m+18, 62m+20, 62m+22, 62m+24, 62m+26, 62m+28, 62m+30, 62m+32, 62m+34, 62m+36, 62m+38, 62m+40, 62m+42, 62m+44, 62m+46, 62m+48, 62m+50, 62m+52, 62m+54, 62m+56, 62m+58, 62m+60, 64m, 64m+1, 64m+2, 64m+3, 64m+4, 64m+5, 64m+6, 64m+8, 64m+10, 64m+11, 64m+12, 64m+13, 64m+16, 64m+17, 64m+20, 64m+21, 64m+22, 64m+23, 64m+24, 64m+25, 64m+26, 64m+28, 64m+29, 64m+32, 64m+34, 64m+35, 64m+36, 64m+37, 64m+38, 64m+40, 64m+42, 64m+44, 64m+45, 64m+46, 64m+48, 64m+49, 64m+50, 64m+51, 64m+52, 64m+53, 64m+56, 64m+58, 66m, 66m+2, 66m+4, 66m+6, 66m+8, 66m+10, 66m+12, 66m+14, 66m+16, 66m+18, 66m+20, 66m+22, 66m+24, 66m+26, 66m+28, 66m+30, 66m+32, 66m+34, 66m+36, 66m+38, 66m+40, 66m+42, 66m+44, 66m+46, 66m+48, 66m+50, 66m+52, 66m+54, 66m+56, 66m+58, 66m+60, 66m+62, 66m+64, 68m, 68m+1, 68m+2, 68m+4, 68m+5, 68m+6, 68m+8, 68m+9, 68m+10, 68m+12, 68m+13, 68m+14, 68m+16, 68m+17, 68m+18, 68m+20, 68m+21, 68m+22, 68m+24, 68m+25, 68m+26, 68m+28, 68m+29, 68m+30, 68m+32, 68m+33, 68m+34, 68m+36, 68m+37, 68m+38, 68m+40, 68m+41, 68m+42, 68m+44, 68m+45, 68m+46, 68m+48, 68m+49, 68m+50, 68m+52, 68m+53, 68m+54, 68m+56, 68m+57, 68m+58, 68m+60, 68m+61, 68m+62, 68m+64, 68m+65, 68m+66, 70m, 70m+2, 70m+4, 70m+6, 70m+8, 70m+10, 70m+12, 70m+14, 70m+16, 70m+18, 70m+20, 70m+22, 70m+24, 70m+26, 70m+28, 70m+30, 70m+32, 70m+34, 70m+36, 70m+38, 70m+40, 70m+42, 70m+44, 70m+46, 70m+48, 70m+50, 70m+52, 70m+54, 70m+56, 70m+58, 70m+60, 70m+62, 70m+64, 70m+66, 70m+68, 72m, 72m+2, 72m+4, 72m+5, 72m+8, 72m+10, 72m+12, 72m+13, 72m+16, 72m+18, 72m+20, 72m+21, 72m+24, 72m+26, 72m+28, 72m+29, 72m+32, 72m+34, 72m+36, 72m+37, 72m+40, 72m+42, 72m+44, 72m+45, 72m+48, 72m+50, 72m+52, 72m+53, 72m+56, 72m+58, 72m+60, 72m+61, 72m+64, 72m+66, 72m+68, 72m+69, 74m, 74m+2, 74m+4, 74m+6, 74m+8, 74m+10, 74m+12, 74m+14, 74m+16, 74m+18, 74m+20, 74m+22, 74m+24, 74m+26, 74m+28, 74m+30, 74m+32, 74m+34, 74m+36, 74m+38, 74m+40, 74m+42, 74m+44, 74m+46, 74m+48, 74m+50, 74m+52, 74m+54, 74m+56, 74m+58, 74m+60, 74m+62, 74m+64, 74m+66, 74m+68, 74m+70, 74m+72, 76m, 76m+1, 76m+2, 76m+4, 76m+5, 76m+6, 76m+8, 76m+9, 76m+10, 76m+12, 76m+13, 76m+14, 76m+16, 76m+17, 76m+18, 76m+20, 76m+21, 76m+22, 76m+24, 76m+25, 76m+26, 76m+28, 76m+29, 76m+30, 76m+32, 76m+33, 76m+34, 76m+36, 76m+37, 76m+38, 76m+40, 76m+41, 76m+42, 76m+44, 76m+45, 76m+46, 76m+48, 76m+49, 76m+50, 76m+52, 76m+53, 76m+54, 76m+56, 76m+57, 76m+58, 76m+60, 76m+61, 76m+62, 76m+64, 76m+65, 76m+66, 76m+68, 76m+69, 76m+70, 76m+72, 76m+73, 76m+74, 78m, 78m+2, 78m+4, 78m+6, 78m+8, 78m+10, 78m+12, 78m+14, 78m+16, 78m+18, 78m+20, 78m+22, 78m+24, 78m+26, 78m+28, 78m+30, 78m+32, 78m+34, 78m+36, 78m+38, 78m+40, 78m+42, 78m+44, 78m+46, 78m+48, 78m+50, 78m+52, 78m+54, 78m+56, 78m+58, 78m+60, 78m+62, 78m+64, 78m+66, 78m+68, 78m+70, 78m+72, 78m+74, 78m+76, 80m, 80m+1, 80m+2, 80m+3, 80m+4, 80m+5, 80m+6, 80m+8, 80m+10, 80m+12, 80m+13, 80m+16, 80m+17, 80m+18, 80m+19, 80m+20, 80m+21, 80m+22, 80m+24, 80m+26, 80m+28, 80m+29, 80m+32, 80m+33, 80m+34, 80m+35, 80m+36, 80m+37, 80m+38, 80m+40, 80m+42, 80m+44, 80m+45, 80m+48, 80m+49, 80m+50, 80m+51, 80m+52, 80m+53, 80m+54, 80m+56, 80m+58, 80m+60, 80m+61, 80m+64, 80m+65, 80m+66, 80m+67, 80m+68, 80m+69, 80m+70, 80m+72, 80m+74, 80m+76, 80m+77, 82m, 82m+2, 82m+4, 82m+6, 82m+8, 82m+10, 82m+12, 82m+14, 82m+16, 82m+18, 82m+20, 82m+22, 82m+24, 82m+26, 82m+28, 82m+30, 82m+32, 82m+34, 82m+36, 82m+38, 82m+40, 82m+42, 82m+44, 82m+46, 82m+48, 82m+50, 82m+52, 82m+54, 82m+56, 82m+58, 82m+60, 82m+62, 82m+64, 82m+66, 82m+68, 82m+70, 82m+72, 82m+74, 82m+76, 82m+78, 82m+80, 84m, 84m+1, 84m+2, 84m+4, 84m+5, 84m+6, 84m+8, 84m+9, 84m+10, 84m+12, 84m+13, 84m+14, 84m+16, 84m+17, 84m+18, 84m+20, 84m+21, 84m+22, 84m+24, 84m+25, 84m+26, 84m+28, 84m+29, 84m+30, 84m+32, 84m+33, 84m+34, 84m+36, 84m+37, 84m+38, 84m+40, 84m+41, 84m+42, 84m+44, 84m+45, 84m+46, 84m+48, 84m+49, 84m+50, 84m+52, 84m+53, 84m+54, 84m+56, 84m+57, 84m+58, 84m+60, 84m+61, 84m+62, 84m+64, 84m+65, 84m+66, 84m+68, 84m+69, 84m+70, 84m+72, 84m+73, 84m+74, 84m+76, 84m+77, 84m+78, 84m+80, 84m+81, 84m+82, 86m, 86m+2, 86m+4, 86m+6, 86m+8, 86m+10, 86m+12, 86m+14, 86m+16, 86m+18, 86m+20, 86m+22, 86m+24, 86m+26, 86m+28, 86m+30, 86m+32, 86m+34, 86m+36, 86m+38, 86m+40, 86m+42, 86m+44, 86m+46, 86m+48, 86m+50, 86m+52, 86m+54, 86m+56, 86m+58, 86m+60, 86m+62, 86m+64, 86m+66, 86m+68, 86m+70, 86m+72, 86m+74, 86m+76, 86m+78, 86m+80, 86m+82, 86m+84, 88m, 88m+2, 88m+4, 88m+5, 88m+8, 88m+10, 88m+12, 88m+13, 88m+16, 88m+18, 88m+20, 88m+21, 88m+24, 88m+26, 88m+28, 88m+29, 88m+32, 88m+34, 88m+36, 88m+37, 88m+40, 88m+42, 88m+44, 88m+45, 88m+48, 88m+50, 88m+52, 88m+53, 88m+56, 88m+58, 88m+60, 88m+61, 88m+64, 88m+66, 88m+68, 88m+69, 88m+72, 88m+74, 88m+76, 88m+77, 88m+80, 88m+82, 88m+84, 88m+85, 90m, 90m+2, 90m+4, 90m+6, 90m+8, 90m+10, 90m+12, 90m+14, 90m+16, 90m+18, 90m+20, 90m+22, 90m+24, 90m+26, 90m+28, 90m+30, 90m+32, 90m+34, 90m+36, 90m+38, 90m+40, 90m+42, 90m+44, 90m+46, 90m+48, 90m+50, 90m+52, 90m+54, 90m+56, 90m+58, 90m+60, 90m+62, 90m+64, 90m+66, 90m+68, 90m+70, 90m+72, 90m+74, 90m+76, 90m+78, 90m+80, 90m+82, 90m+84, 90m+86, 90m+88, 92m, 92m+1, 92m+2, 92m+4, 92m+5, 92m+6, 92m+8, 92m+9, 92m+10, 92m+12, 92m+13, 92m+14, 92m+16, 92m+17, 92m+18, 92m+20, 92m+21, 92m+22, 92m+24, 92m+25, 92m+26, 92m+28, 92m+29, 92m+30, 92m+32, 92m+33, 92m+34, 92m+36, 92m+37, 92m+38, 92m+40, 92m+41, 92m+42, 92m+44, 92m+45, 92m+46, 92m+48, 92m+49, 92m+50, 92m+52, 92m+53, 92m+54, 92m+56, 92m+57, 92m+58, 92m+60, 92m+61, 92m+62, 92m+64, 92m+65, 92m+66, 92m+68, 92m+69, 92m+70, 92m+72, 92m+73, 92m+74, 92m+76, 92m+77, 92m+78, 92m+80, 92m+81, 92m+82, 92m+84, 92m+85, 92m+86, 92m+88, 92m+89, 92m+90, 94m, 94m+2, 94m+4, 94m+6, 94m+8, 94m+10, 94m+12, 94m+14, 94m+16, 94m+18, 94m+20, 94m+22, 94m+24, 94m+26, 94m+28, 94m+30, 94m+32, 94m+34, 94m+36, 94m+38, 94m+40, 94m+42, 94m+44, 94m+46, 94m+48, 94m+50, 94m+52, 94m+54, 94m+56, 94m+58, 94m+60, 94m+62, 94m+64, 94m+66, 94m+68, 94m+70, 94m+72, 94m+74, 94m+76, 94m+78, 94m+80, 94m+82, 94m+84, 94m+86, 94m+88, 94m+90, 94m+92, 96m, 96m+1, 96m+2, 96m+3, 96m+4, 96m+5, 96m+6, 96m+8, 96m+10, 96m+11, 96m+12, 96m+13, 96m+14, 96m+16, 96m+17, 96m+18, 96m+19, 96m+20, 96m+21, 96m+22, 96m+23, 96m+24, 96m+25, 96m+26, 96m+28, 96m+29, 96m+32, 96m+33, 96m+34, 96m+35, 96m+36, 96m+37, 96m+38, 96m+40, 96m+42, 96m+43, 96m+44, 96m+45, 96m+46, 96m+48, 96m+49, 96m+50, 96m+51, 96m+52, 96m+53, 96m+54, 96m+55, 96m+56, 96m+57, 96m+58, 96m+60, 96m+61, 96m+64, 96m+65, 96m+66, 96m+67, 96m+68, 96m+69, 96m+70, 96m+72, 96m+74, 96m+75, 96m+76, 96m+77, 96m+78, 96m+80, 96m+81, 96m+82, 96m+83, 96m+84, 96m+85, 96m+86, 96m+87, 96m+88, 96m+89, 96m+90, 96m+92, 96m+93, 98m, 98m+2, 98m+4, 98m+6, 98m+8, 98m+10, 98m+12, 98m+14, 98m+16, 98m+18, 98m+20, 98m+22, 98m+24, 98m+26, 98m+28, 98m+30, 98m+32, 98m+34, 98m+36, 98m+38, 98m+40, 98m+42, 98m+44, 98m+46, 98m+48, 98m+50, 98m+52, 98m+54, 98m+56, 98m+58, 98m+60, 98m+62, 98m+64, 98m+66, 98m+68, 98m+70, 98m+72, 98m+74, 98m+76, 98m+78, 98m+80, 98m+82, 98m+84, 98m+86, 98m+88, 98m+90, 98m+92, 98m+94, 98m+96, 100m, 100m+1, 100m+2, 100m+4, 100m+5, 100m+6, 100m+8, 100m+9, 100m+10, 100m+12, 100m+13, 100m+14, 100m+16, 100m+17, 100m+18, 100m+20, 100m+21, 100m+22, 100m+24, 100m+25, 100m+26, 100m+28, 100m+29, 100m+30, 100m+32, 100m+33, 100m+34, 100m+36, 100m+37, 100m+38, 100m+40, 100m+41, 100m+42, 100m+44, 100m+45, 100m+46, 100m+48, 100m+49, 100m+50, 100m+52, 100m+53, 100m+54, 100m+56, 100m+57, 100m+58, 100m+60, 100m+61, 100m+62, 100m+64, 100m+65, 100m+66, 100m+68, 100m+69, 100m+70, 100m+72, 100m+73, 100m+74, 100m+76, 100m+77, 100m+78, 100m+80, 100m+81, 100m+82, 100m+84, 100m+85, 100m+86, 100m+88, 100m+89, 100m+90, 100m+92, 100m+93, 100m+94, 100m+96, 100m+97, 100m+98, 102m, 102m+2, 102m+4, 102m+6, 102m+8, 102m+10, 102m+12, 102m+14, 102m+16, 102m+18, 102m+20, 102m+22, 102m+24, 102m+26, 102m+28, 102m+30, 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