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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
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
Sequence in context: A226261 A028696 A284874 * A293782 A153729 A357972
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 March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)