A238338 Encoded bases for which A214424(n) is palindromic.

13, 26, 13, 47, 28, 46, 24, 17, 25, 14, 19, 47, 17, 34, 68, 13, 24, 46, 45, 17, 46, 28, 49, 28, 56, 14, 45, 19, 45, 37, 16, 48, 59, 46, 14, 18, 15, 56, 59, 26, 36, 29, 25, 37, 69, 28, 28, 56, 47, 68, 58, 29, 35, 17, 78, 48, 49, 68, 19, 27, 79, 46, 59, 37, 28, 17

Offset

1,1

Comments

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.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Attila Bérczes and Volker Ziegler, On simultaneous palindromes, arXiv 1403.0787, Mar 04 2014

Edray Herber Goins, Palindromes in different bases: a conjecture of J. Ernest Wilkins, Integers, Vol. 9 (2009), A55

Mathematica

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

Crossrefs

Cf. A214423, A214424, A214427.

Sequence in context: A123827 A105796 A226051 * A040156 A296752 A297279

Adjacent sequences: A238335 A238336 A238337 * A238339 A238340 A238341

Keyword

nonn,base

Author

T. D. Noe, Mar 07 2014

Status

approved