A238338 - OEIS

%I #17 Oct 30 2023 07:26:33

%S 13,26,13,47,28,46,24,17,25,14,19,47,17,34,68,13,24,46,45,17,46,28,49,

%T 28,56,14,45,19,45,37,16,48,59,46,14,18,15,56,59,26,36,29,25,37,69,28,

%U 28,56,47,68,58,29,35,17,78,48,49,68,19,27,79,46,59,37,28,17

%N Encoded bases for which A214424(n) is palindromic.

%C The two bases b < c are encoded as one number (b-1)*10 + (c-1). Similar to A214427 which tabulates the single base for which A214423(n) is palindromic. In the first 1000 terms, the base pairs (2,4), (2,8), (3,9), and (4,8) are most common, occurring 148, 227, 166, and 94 times, respectively. The base pair (2,3) occurs only once.

%H Giovanni Resta, <a href="/A238338/b238338.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)

%H Attila Bérczes and Volker Ziegler, <a href="http://arxiv.org/abs/1403.0787">On simultaneous palindromes</a>, arXiv 1403.0787, Mar 04 2014

%H 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

%t n = -1; t = {}; While[Length[t] < 100, n++; If[Count[c = Table[s = IntegerDigits[n, m]; s == Reverse[s], {m, 2, 10}], True] == 2, d = Flatten[Position[c, True]]; AppendTo[t, 10*d[[1]] + d[[2]]]]]; t

%Y Cf. A214423, A214424, A214427.

%K nonn,base

%O 1,1

%A _T. D. Noe_, Mar 07 2014