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A216841 Smallest palindromic number of length 2 in two bases differing by n. 16
24, 18, 8, 10, 12, 14, 16, 18, 15, 22, 18, 26, 21, 30, 24, 34, 24, 38, 30, 28, 33, 46, 32, 50, 39, 36, 35, 58, 40, 62, 40, 44, 51, 70, 45, 74, 57, 52, 48, 82, 56, 86, 55, 54, 69, 94, 60, 98, 60, 68, 65, 106, 63, 66, 70, 76, 87, 118, 70, 122, 93, 84, 80, 78, 77 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 2..10000

EXAMPLE

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.

a(10) = 15 is 33 in base 4 and 11 in base 14. - Chai Wah Wu, Aug 19 2015

CROSSREFS

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.

Sequence in context: A226261 A028696 A284874 * A293782 A153729 A128560

Adjacent sequences:  A216838 A216839 A216840 * A216842 A216843 A216844

KEYWORD

nonn,base

AUTHOR

James G. Merickel, Sep 19 2012

EXTENSIONS

More terms and corrected a(10) from Chai Wah Wu, Aug 19 2015

STATUS

approved

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Last modified December 16 06:18 EST 2019. Contains 330016 sequences. (Running on oeis4.)