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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.

%I A293925 #85 Jan 12 2023 01:55:13
%S A293925 6643,5,10,31,26,46,7,28,21,67,85,8,85,24,92,9,121,63,18,154,121,127,
%T A293925 10,10,109,80,40,154,33,121,55,88,55,121,121,191,255,244,255,12,166,
%U A293925 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
%N 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.
%H A293925 Michel Marcus, <a href="/A293925/b293925.txt">Rows 3..100 of triangle, flattened</a>
%H A293925 Jean-Paul Delahaye, <a href="http://www.pourlascience.fr/ewb_pages/a/article-les-nombres-palindromes-38761.php">121, 404 et autres nombres palindromes</a> (in French), Pour La Science, 480, October 2017.
%H A293925 Erich Friedman, <a href="https://erich-friedman.github.io/mathmagic/0699.html">Problem of the Month</a>, June 1999. "Does there exist an integer which is a palindrome in any pair of bases n and k?"
%e A293925 Triangle begins:
%e A293925   6643,
%e A293925      5,  10,
%e A293925     31,  26, 46,
%e A293925      7,  28, 21, 67,
%e A293925     85,   8, 85, 24,  92,
%e A293925      9, 121, 63, 18, 154, 121,
%e A293925   ...
%t A293925 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 *)
%o A293925 (PARI) isok(j, n, k) = my(dn=digits(j,n), dk=digits(j,k)); (Vecrev(dn)==dn) && (Vecrev(dk)==dk);
%o A293925 T(n,k) = {j = max(n,k); while(! isok(j, n, k), j++); j;}
%o A293925 tabl(nn) = for (n=3, nn, for (k=2, n-1, print1(T(n,k), ", ")); print);
%Y A293925 Cf. A048268 (right diagonal), A056749 (1st column).
%K A293925 nonn,base,tabl
%O A293925 3,1
%A A293925 _Michel Marcus_, Nov 16 2017