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 A293925 Triangle read by rows T(n, k) is the least integer that is a palindrome in base n and k, with more than 1 digit in both bases, n >= 3 and 2 <= k < n. 1
 6643, 5, 10, 31, 26, 46, 7, 28, 21, 67, 85, 8, 85, 24, 92, 9, 121, 63, 18, 154, 121, 127, 10, 10, 109, 80, 40, 154, 33, 121, 55, 88, 55, 121, 121, 191, 255, 244, 255, 12, 166, 24, 36, 60, 232, 65, 13, 65, 26, 104, 78, 65, 91, 181, 277, 313, 28, 42, 98, 14, 235, 154, 70, 222, 84, 326 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Michel Marcus, Rows 3..100 of triangle, flattened Jean-Paul Delahaye, 121, 404 et autres nombres palindromes (in French), Pour La Science, 480, October 2017. Erich Friedman, Problem of the Month, June 1999. "Does there exist an integer which is a palindrome in any pair of bases n and k?" EXAMPLE Triangle begins: 6643, 5, 10, 31, 26, 46, 7, 28, 21, 67, 85, 8, 85, 24, 92, 9, 121, 63, 18, 154, 121, ... MATHEMATICA palQ[n_Integer, base_Integer] := Block[{}, Reverse[idn = IntegerDigits[n, base]] == idn]; Table[ t[n, k], {n, 3, 13}, {k, 2, n - 1}] // Flatten (* Robert G. Wilson v, Nov 17 2017 *) PROG (PARI) isok(j, n, k) = my(dn=digits(j, n), dk=digits(j, k)); (Vecrev(dn)==dn) && (Vecrev(dk)==dk); T(n, k) = {j = max(n, k); while(! isok(j, n, k), j++); j; } tabl(nn) = for (n=3, nn, for (k=2, n-1, print1(T(n, k), ", ")); print); CROSSREFS Cf. A048268 (right diagonal), A056749 (1st column). Sequence in context: A345571 A345827 A196510 * A048268 A043634 A060792 Adjacent sequences: A293922 A293923 A293924 * A293926 A293927 A293928 KEYWORD nonn,base,tabl AUTHOR Michel Marcus, Nov 16 2017 STATUS approved

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Last modified May 28 08:47 EDT 2023. Contains 362999 sequences. (Running on oeis4.)