A030547 Number of terms (including the initial term) needed to reach a palindrome when the Reverse Then Add! map (x -> x + (x-with-digits-reversed)) is repeatedly applied to n, or -1 if a palindrome is never reached.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 2, 2, 2, 2, 1, 2, 3, 3, 4, 2, 2, 2, 2, 3, 2, 1, 3, 4, 5, 2, 2, 2, 3, 2, 3, 3, 1, 5, 7, 2, 2, 3, 2, 3, 3, 4, 5, 1, 25, 2, 3, 2, 3, 3, 4, 5, 7, 25

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Comments

It is conjectured that a(196) is the smallest term equal to -1. See A023108.

References

• Daniel Lignon, Dictionnaire de (presque) tous les nombres entiers, Ellipses, Paris, 2012, 702 pages. See Entry 196.

Links

• Eric Weisstein's World of Mathematics, 196 Algorithm.

Crossrefs

Cf. A006960, A023108, A063018, etc.

Equals A033665(n) + 1.

Programs

Mathematica

Table[Length@
  NestWhileList[# + IntegerReverse[#] &, n, ! PalindromeQ[#]  &], {n, 98}] (* Robert Price, Oct 18 2019 *)

Extensions

Edited by N. J. A. Sloane, May 09 2015