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Numbers n such that 17 applications of 'Reverse and Subtract' lead to n, whereas fewer than 17 applications do not lead to n.
18

%I #12 Sep 24 2020 02:57:31

%S 1186781188132188,1464465185355348,2178772178212278,2191191178088088,

%T 2196702178032978,2202202177977978,2334334176656658,3041250269587497,

%U 4361064356389356,4906609350933906,6232232537677674,6543356534566434

%N Numbers n such that 17 applications of 'Reverse and Subtract' lead to n, whereas fewer than 17 applications do not lead to n.

%C There are 17 sixteen-digit terms in the sequence. Further terms are obtained (a) by inserting at the center of these terms any number of 9's 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.

%C This is a working sequence. It is neither by computation nor by proof guaranteed that there are no smaller or interleaved terms.

%C All terms are divisible by 1099999989. - _Hugo Pfoertner_, Sep 23 2020

%H Ray Chandler, <a href="/A072719/b072719.txt">Table of n, a(n) for n = 1..17</a>

%F n = f^17(n), n <> f^k(n) for k < 17, where f: x -> |x - reverse(x)|.

%e 1186781188132188 -> 7625537623744623 -> 4361064356389356 -> 2178772178212278 -> 6543356534566434 -> 2196702178032978 -> 6595606534043934 -> 2202202177977978 -> 6595595534044044 -> 2191191178088088 -> 6617617533823824 -> 2334334176656658 -> 6232232537677674 -> 1464465185355348 -> 6971070630289293 -> 3041250269587497 -> 4906609350933906 -> 1186781188132188.

%Y Cf. A072137, A072141, A072142, A072143, A072718.

%K base,nonn

%O 1,1

%A _Klaus Brockhaus_, Jul 15 2002