Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Apr 08 2020 00:06:42
%S 1,2,3,4,5,6,7,9,99,999,9999,99999,999999,9999999,99999999,999999999,
%T 9999999999,99999999999,999999999999,9999999999999,99999999999999,
%U 999999999999999,9999999999999999,99999999999999999
%N Palindromes k such that k + 2 is also a palindrome.
%C Perhaps from 8th term onwards the only members are a(n) = 10^(n-7) - 1 for n > 7.
%C 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
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Apr 13 2003
%E Incorrect formula removed by _Felix Fröhlich_, Jul 24 2014
%E More terms from _Felix Fröhlich_, Jul 24 2014