A109871 Number of ways a number can be expressed as the difference of two palindromes, or -1 if this number if infinite.

9, -1, 8, 7, 6, 5, 4, 3, 2, 82, -1, 2, 2, 1, 1, 1, 1, 1, 1, 73, 17, 10, 1, 2, 1, 1, 1, 1, 1, 64, 25, 3, 8, 1, 2, 1, 1, 1, 1, 55, 33, 3, 2, 7, 1, 2, 1, 1, 1, 46, 41, 3, 2, 2, 6, 1, 2, 1, 1, 37, 49, 3, 2, 2, 2, 5, 1, 2, 1, 28, 57, 3, 2, 2, 2, 2, 4, 1, 2, 19, 65, 3, 2, 2, 2, 2, 2, 3, 1, 11, 73, 4, 3, 3, 3, 3, 3, 3, 3, 812

Offset

1,1

Comments

2 = (10^k+1)-(10^k-1) where (10^k+1) and (10^k-1) are palindromes for all k. 11 = (2*10^k +2)-(2*10^k-9)where (2*10^k+2) and (2*10^k-9) are palindromes for all k. Hence a(2) = a(11)are denoted by -1. Note: terms should be checked for any errors.

The differences that occur infinitely many times are 2 and 11*10^k (k >= 0). - David Wasserman, Apr 03 2008

Links

Table of n, a(n) for n=1..100.

Example

a(2) = a(11) = -1 as 2 and 11 can be so expressed infinitely many times.
a(22) = 9, 22 = 22-0, 33-11, 44-22, 55-33, 66-44, 77-55, 88-66, 99-77, 121-99.
a(22) = 10 because 22 = 22-0, 33-11, 44-22, 55-33, 66-44, 77-55, 88-66, 99-77, 121-99 and 1001-979.

Crossrefs

Cf. A109870.

Sequence in context: A011111 A301815 A191502 * A087500 A238168 A340551

Adjacent sequences: A109868 A109869 A109870 * A109872 A109873 A109874

Keyword

base,sign

Author

Amarnath Murthy, Jul 09 2005

Extensions

Corrected and extended by David Wasserman, Apr 03 2008

Status

approved