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A171740
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The first number palindromic with n digits in more than one base (shown in base 10).
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22
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1, 8, 26, 624, 2293, 207702, 186621, 342324801, 27924649, 260311602096, 1556085529, 248876637484140, 318713056300, 2544221971606336, 4712469842177, 530386561769238496, 1939137135947326
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OFFSET
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1,2
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COMMENTS
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This sequence gives the first value (represented in base 10) that is palindromic -- i.e., the same when its digits are reflected about the center -- with n >= 1 digits in two different bases.
Currently waiting on doubly 18-palindrome. The 19-palindrome is one in bases 10 and 11, 6411682614162861146 in base 10. For some time I was laboring under the impression that the new terms now added -- starting at 9-palindromes -- were too difficult to find, thinking a change I recently made would not increase programming efficiency as much as it did. The results come from the research done for the sequences labeled with A216*** shown below. The other cross-referenced sequences, A171***, deal with higher orders of multiplicity and such things. - James G. Merickel, Sep 19 2012
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LINKS
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EXAMPLE
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a(2)=8 is 11 in base 7 and 22 in base 3.
a(3)=26 is 101 in base 5 and 222 in base 3.
a(4)=624 is 1551 in base 7 and 4444 in base 5.
a(7)=186621 is 3555553 in base 6 and 1405041 in base 7.
a(8)=342324801 is 96788769 in base 12 and 14677641 in base 16.
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CROSSREFS
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Cf. A171701, A171702, A171703, A171704, A171705, A171706, A171741, A171742, A216840, A216841, A216843, A216899, A216900, A216901, A216902, A216903, A216904, A216905, A216906, A216907, A216908, A216909, A216910.
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KEYWORD
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more,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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