A065001 a(n) = (presumed) number of palindromes in the 'Reverse and Add!' trajectory of n, or -1 if this number is not finite.

11, 10, 8, 9, 10, 7, 6, 8, 4, 9, 9, 6, 7, 5, 5, 7, 6, 3, 4, 8, 6, 8, 5, 5, 7, 6, 3, 4, 4, 6, 7, 5, 6, 7, 6, 3, 4, 4, 4, 7, 5, 5, 7, 7, 3, 4, 4, 4, 2, 5, 5, 7, 6, 3, 5, 4, 4, 2, 6, 5, 7, 6, 3, 4, 4, 5, 2, 6, 3, 7, 6, 3, 4, 4, 4, 2, 7, 3, 5, 6, 3, 4, 4, 4, 2, 6, 3, 6, 1, 3, 4, 4, 4, 2, 6, 3, 5, 1, 3, 8, 8, 6, 6

Offset: 1

Author

Klaus Brockhaus, Nov 01 2001

Keywords

• base
• nonn

Comments

Presumably a(196) = 0 (see A016016). Conjecture: There is no n > 0 such that the trajectory of n contains an infinite number of palindromes; the trajectory of n eventually leads to a term in the trajectory of some integer k which belongs to sequence A063048, i.e. whose trajectory (presumably) never leads to a palindrome.

Examples

			8, 77, 1111, 2222, 4444, 8888, 661166, 3654563 are the eight palindromes in the trajectory of 8 and 3654563 + 3654563 = 7309126 is the sixth term in the trajectory of 10577 (see A063433) which (presumably) never leads to a palindrome (see A063048), so a(8) = 8.
		

Links

• Index entries for sequences related to Reverse and Add!

Crossrefs

A002113, A016016, A033865, A023108, A063048, A063433.

Programs

ARIBAS

maxarg := 120; stop := 500; for k := 1 to maxarg do n := k; count := 0; c := 0; while c < stop do if n = int_reverse(n) then inc(count); c := 0; end; inc(c); n := n + int_reverse(n); end; write(count," " ); end;