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A171740 The first number palindromic with n digits in more than one base (shown in base 10). 22
1, 8, 26, 624, 2293, 207702, 186621, 342324801, 27924649, 260311602096, 1556085529, 248876637484140, 318713056300, 2544221971606336, 4712469842177, 530386561769238496, 1939137135947326 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=1..17.


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.


Cf. A171701, A171702, A171703, A171704, A171705, A171706, A171741, A171742, A216840, A216841, A216843, A216899, A216900, A216901, A216902, A216903, A216904, A216905, A216906, A216907, A216908, A216909, A216910.

Sequence in context: A240291 A203635 A000810 * A129663 A112646 A119522

Adjacent sequences:  A171737 A171738 A171739 * A171741 A171742 A171743




James G. Merickel, Dec 17 2009


Corrected typo in example by Chai Wah Wu, Jul 18 2015



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Last modified December 15 17:03 EST 2019. Contains 330000 sequences. (Running on oeis4.)