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

Author

Michel Marcus, Nov 16 2017

Keywords

• nonn
• base
• tabl

Examples

			Triangle begins:
  6643,
     5,  10,
    31,  26, 46,
     7,  28, 21, 67,
    85,   8, 85, 24,  92,
     9, 121, 63, 18, 154, 121,
  ...
		

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?"

Crossrefs

Cf. A048268 (right diagonal), A056749 (1st column).

Programs

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 *)

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);