A225538 Let r(n) denote the reverse of n. For every n, consider the sequence n_1 = n + 1 + r(n+1), and for m >= 2, n_m = n_(m-1) + 1 + r(n_(m-1) + 1). a(n) is the least m for which n_m is a palindrome, or 0 if there is no such m.

1, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 4, 1, 1, 1, 1, 2, 1, 2, 2, 4, 7, 1, 1, 1, 2, 1, 2, 2, 4, 7, 10, 1, 1, 2, 1, 2, 2, 4, 7

Offset

0,5

Comments

Conjecture: the least n's for which a(n) = 0 are 1895, 1985, 2894, 2984, 3893, and 3983. - Peter J. C. Moses, May 10 2013

See analogous numbers in A023108 for which the so-called Lychrel process "Reverse and Add!", apparently, never leads to a palindrome.

Links

Peter J. C. Moses, Table of n, a(n) for n = 0..5000

Example

For n=8, 9 + 9 = 18, 19 + 91 = 110, 111 + 111 = 222 is a palindrome. Thus a(8)=3.

Crossrefs

Cf. A023108.

Sequence in context: A343121 A090872 A283472 * A212355 A238646 A194330

Adjacent sequences: A225535 A225536 A225537 * A225539 A225540 A225541

Keyword

nonn,base

Author

Vladimir Shevelev, May 10 2013

Status

approved