| QUOTE |
| A Lychrel number is a natural number which cannot form a palindrome through the iterative process of repeatedly reversing its base 10 digits and adding the resulting numbers. This process is called the 196-algorithm. The name "Lychrel" was coined by Wade VanLandingham – a rough anagram of his girlfriend's name Cheryl. No Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. |
Of course, the concept can extend to other bases as well. For example, in dozenal, the following numbers do not produce palindromes within *100 iterations:
179 1B9 278 2B8 377 3B7 476 4B6 674 6B4 773 7B3 872 8B2 971 9B1 A2B A3B A5B A70 AAB AB0 B2A B3A B5A BAA 13B9 14A9 1599 15B9 1689 16A9 1779 1799 1869 1889 18B9 1959 1979 19A9 19B9 1A49 1A69 1A99 1AA9 1B39 1B59 1B89 1B99 1BB9 23B8 24A8 2598 25B8 2688 26A8 2778 2798 2868 2888 28B8 2958 2978 29A8 29B8 2A48 2A68 2A98 2AA8 2B38 2B58 2B88 2B98 2BB8 2BBB 33B7 34A7 3597 35B7 3687 36A7 3777 3797 3867 3887 38B7 3957 3977 39A7 39B7 3A47 3A67 3A97 3AA7 3B37 3B57 3B87 3B97 3BB7 3BBA 43B6 44A6 4596 45B6 4686 46A6 4776 4796 4866 4886 48B6 4956 4976 49A6 49B6 4A46 4A66 4A96 4AA6 4B36 4B56 4B86 4B96 4BB6 4BB9 53B5 54A5 5595 55B5 5685 56A5 5795 5865 58B5 5955 5975 59A5 59B5 5A45 5A65 5A95 5B35 5B55 5B85 5B95 5BB8 63B4 64A4 6594 65B4 6684 66A4 6774 6794 6864 6884 68B4 6954 6974 69A4 69B4 6A44 6A64 6A94 6AA4 6B34 6B54 6B84 6B94 6BB4 6BB7 73B3 74A3 7593 75B3 7683 76A3 7773 7793 7863 7883 78B3 7953 7973 79A3 79B3 7A43 7A63 7A93 7AA3 7B33 7B53 7B83 7B93 7BB3 7BB6 83B2 84A2 8592 85B2 8682 86A2 8772 8792 8862 8882 88B2 8952 8972 89A2 89B2 8A42 8A62 8A92 8AA2 8B32 8B52 8B82 8B92 8BB2 8BB5 93B1 94A1 9591 95B1 9681 96A1 9771 9791 9861 9881 98B1 9951 9971 99A1 99B1 9A41 9A61 9A91 9AA1 9B31 9B51 9B81 9B91 9BB1 9BB4 A04B A05B A06B A09B A0AB A13B A14B A15B A18B A19B A22B A23B A24B A27B A28B A31B A32B A33B A36B A37B A3B0 A40B A41B A42B A45B A46B A4A0 A4BB A50B A51B A54B A55B A590 A5AB A5B0 A5BB A60B A63B A64B A680 A69B A6A0 A6AB A6BB A72B A73B A770 A78B A790 A79B A7AB A81B A82B A860 A87B A880 A88B A89B A8B0 A90B A91B A950 A96B A970 A97B A98B A9A0 A9B0 A9BB AA0B AA40 AA5B AA60 AA6B AA7B AA90 AAA0 AAAB AABB AB30 AB4B AB50 AB5B AB6B AB80 AB90 AB9B ABAB ABB0 ABB3 B04A B05A B06A B07B B09A B0AA B0AB B13A B14A B15A B16B B18A B19A B19B B22A B23A B24A B25B B27A B28A B28B B31A B32A B33A B34B B36A B37A B37B B40A B41A B42A B43B B45A B46A B46B B4BA B50A B51A B52B B54A B55A B5AA B5BA B60A B61B B63A B64A B64B B69A B6AA B6BA B70B B72A B73A B73B B78A B79A B7AA B7BB B81A B82A B82B B87A B88A B89A B8AB B90A B91A B91B B96A B97A B98A B9BA BA0A BA0B BA5A BA6A BA7A BA8B BAAA BABA BABB BB4A BB5A BB6A BB7B BB9A BBAA BBAB BBB2
Can you find any patterns? Or a base in which there are no Lychrel numbers?