This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A214424 #34 Jun 29 2024 09:09:44
%S A214424 15,16,17,18,20,24,26,27,28,31,33,36,45,46,50,51,52,57,67,73,78,82,88,
%T A214424 91,92,93,98,99,104,105,107,109,111,114,119,127,129,135,141,142,150,
%U A214424 151,160,170,171,173,182,185,186,200,209,212,215,219,227,246,252
%N A214424 Numbers that are palindromic in exactly two bases b, 2 <= b <= 10.
%C A214424 Every pair of bases occurs. The pair (2,3), for the number a(732) = 1422773, is the last to occur. Note that 1422773 = 101011011010110110101(2) = 2200021200022(3).
%C A214424 See A238338 for the pairs of bases. - _T. D. Noe_, Mar 07 2014
%H A214424 Giovanni Resta, <a href="/A214424/b214424.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A214424 Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On simultaneous palindromes</a>, arXiv 1403.0787 [math.NT], 2014.
%H A214424 Edray Herber Goins, <a href="http://www.emis.de/journals/INTEGERS/papers/j55/j55.Abstract.html">Palindromes in different bases: a conjecture of J. Ernest Wilkins</a>, Integers, Vol. 9 (2009), A55.
%F A214424 A050812(a(n)) = 2.
%e A214424 15 is palindromic in bases 2 and 4: 15 = 1111_2 = 33_4.
%t A214424 n = -1; t = {}; While[Length[t] < 100, n++; If[Count[Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 2, AppendTo[t, n]]]; t
%o A214424 (PARI) pal(v)=v==Vecrev(v)
%o A214424 is(n)=sum(b=2,10,pal(digits(n,b)))==2 \\ _Charles R Greathouse IV_, Mar 05 2014
%Y A214424 Cf. A050813, A214423, A214425, A214426 (palindromic in 0-1 and 3-4 bases).
%K A214424 nonn,base
%O A214424 1,1
%A A214424 _T. D. Noe_, Jul 18 2012