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A082274 Palindromes k such that k + 2 is also a palindrome. 1
1, 2, 3, 4, 5, 6, 7, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999 (list; graph; refs; listen; history; text; internal format)



Perhaps from 8th term onwards the only members are a(n) = 10^(n-7) - 1 for n > 7.

The above conjecture is true. Adding two to the least significant digit of a number can result in a carry of at most 1, which only happens if the digit of least significance is 8 or 9. If the least significant digit is 8, adding two results in that digit becoming 0, so the resulting number can't be palindromic. If only the k least and most significant digits are 9, the least significant digit will become 1 and all other adjacent digits 9 will turn into the digit 0 and produce a carry of 1. For the starting number to have been palindromic, the k most significant digits must also be 9's. Any digits that are not 9's between the 9's will not produce a carry on their own when increased by one through the previous carry, resulting in a nonpalindromic number with some 9's as most significant digits and a single 1 and 0's as least significant digits. - Felix Fröhlich, Jul 22 2014


Table of n, a(n) for n=1..24.


Sequence in context: A037405 A048333 A007496 * A029804 A084690 A194963

Adjacent sequences:  A082271 A082272 A082273 * A082275 A082276 A082277




Amarnath Murthy, Apr 13 2003


Incorrect formula removed by Felix Fröhlich, Jul 24 2014

More terms from Felix Fröhlich, Jul 24 2014



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Last modified September 21 00:38 EDT 2020. Contains 337265 sequences. (Running on oeis4.)