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.

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

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