%I #23 Aug 22 2015 00:49:04
%S 24,18,8,10,12,14,16,18,15,22,18,26,21,30,24,34,24,38,30,28,33,46,32,
%T 50,39,36,35,58,40,62,40,44,51,70,45,74,57,52,48,82,56,86,55,54,69,94,
%U 60,98,60,68,65,106,63,66,70,76,87,118,70,122,93,84,80,78,77
%N Smallest palindromic number of length 2 in two bases differing by n.
%C This and other sequences in this collection -- that runs through 17-digit palindromes but (for now) excludes 16-digit ones (but see A216910) -- have offset 2 because an even-length palindrome in one base ends in 0 in the base one larger. After its first two terms, this particular sequence in the collection is trivial. The collection in its entirety are the A216*** cross-references plus this one. The smaller of the pair of bases here are (in sequence) 5, 5, 3, 4, 5, 6, 7, 8, 9. Aside from the first two sequences being switched in order of their A-numbers, the others are in order (but note that only the last 12 are without gaps in the A-sequencing). The A171*** cross-references are to a variety of record small multi-base palindromes.
%H Chai Wah Wu, <a href="/A216841/b216841.txt">Table of n, a(n) for n = 2..10000</a>
%e All numbers smaller than 24 (in base 10) fail to have two bases differing by 2 in which the number is a 2-digit palindrome. Decimal number 24 is 44 in base 5 and is 33 in base 7. Similarly, for the second term here, the facts that decimal number 18 is 33 in base 5 and 22 in base 8 and that no smaller number than decimal 18 has 2 bases in which it is a 2-digit palindrome result in its position here.
%e a(10) = 15 is 33 in base 4 and 11 in base 14. - _Chai Wah Wu_, Aug 19 2015
%Y Cf. A171701, A171702, A171703, A171704, A171705, A171706, A171740, A171741, A171742, A171775, A216840, A216843, A216899, A216900, A216901, A216902, A216903, A216904, A216905, A216906, A216907, A216908, A216909, A216910.
%K nonn,base
%O 2,1
%A _James G. Merickel_, Sep 19 2012
%E More terms and corrected a(10) from _Chai Wah Wu_, Aug 19 2015