A082274 Palindromes k such that k + 2 is also a palindrome.

1, 2, 3, 4, 5, 6, 7, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999

Offset

1,2

Comments

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

Links

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

Crossrefs

Sequence in context: A037405 A048333 A007496 * A029804 A084690 A368431

Adjacent sequences: A082271 A082272 A082273 * A082275 A082276 A082277

Keyword

base,nonn

Author

Amarnath Murthy, Apr 13 2003

Extensions

Incorrect formula removed by Felix Fröhlich, Jul 24 2014

More terms from Felix Fröhlich, Jul 24 2014

Status

approved