A072138 Smallest k whose 'Reverse and Subtract' trajectory has a preperiodic part of length n.

0, 1, 10, 16, 14, 15, 13, 1011, 1017, 1037, 1027, 1014, 1013, 1028, 100113, 100104, 100145, 100134, 100103, 100112, 100133, 100187, 100114, 100128, 100194, 100107, 100307, 100277, 100413, 100345, 100429, 100215, 100427, 100214, 100433, 100335

Offset: 0

Author

Klaus Brockhaus, Jun 24 2002

Keywords

• base
• nonn

Comments

'Reverse and Subtract' (cf. A072137) is defined by x -> |x - reverse(x)|. For small n the last term of the preperiodic part of the trajectory (cf. A072139) is a palindrome, so this sequence is a weak analog of A033665, which uses 'Reverse and Add'. - 1012 is the first n such that last term of the preperiodic part is not palindromic (cf. A072140).

Examples

			a(8) = 1017, since 1017 is the smallest number whose 'Reverse and Subtract' trajectory has eight preperiodic terms: 1017 -> 6084 -> 1278 -> 7443 -> 3996 -> 2997 -> 4995 -> 999.
		

Crossrefs

Cf. A033665, A072137, A072139, A072140, A072146.