A072718 Numbers n such that 12 applications of 'Reverse and Subtract' lead to n, whereas fewer than 12 applications do not lead to n.

118722683079, 138346366158, 178574614218, 277673713317, 316920881277, 336544564356, 435643663455, 455267148336, 614218178574, 633841861653, 713317277673, 851663544732

Offset: 1

Author

Klaus Brockhaus, Jul 15 2002

Keywords

• base
• nonn

Comments

There are 12 twelve-digit terms in the sequence. Further terms are obtained (a) by inserting at the center of these terms either any number of 0's (for 178574614218, 277673713317, 614218178574, 713317277673) or any number of 9's (for the other eight terms) and (b) by concatenating a term any number of times with itself and inserting an equal number of 0's at all junctures. Method (b) may be applied recursively to all terms. - Revised thanks to a comment from Hans Havermann, Jan 27 2004.

Examples

			118722683079 -> 851663544732 -> 614218178574 -> 138346366158 -> 713317277673 -> 336544564356 -> 316920881277 -> 455267148336-> 178574614218-> 633841861653-> 277673713317-> 435643663455-> 118722683079.
		

Crossrefs

Cf. A072137, A072141, A072142, A072143, A072719.

Formula

n = f^12(n), n <> f^k(n) for k < 12, where f: x -> |x - reverse(x)|.