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

1,1

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.

Links

Table of n, a(n) for n=1..103.

Index entries for sequences related to Reverse and Add!

Example

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.

Prog

(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; .

Crossrefs

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

Sequence in context: A078200 A105034 A324153 * A022967 A023453 A261304

Adjacent sequences: A064998 A064999 A065000 * A065002 A065003 A065004

Keyword

base,nonn

Author

Klaus Brockhaus, Nov 01 2001

Status

approved