A292858 Numbers n such that 9 applications of 'Reverse and Subtract' lead to n, whereas fewer than 9 applications do not lead to n.

111603518721165960373027269626940447783074704878, 176512193475025275151977319848516480415708873428, 230594281653466673786238177213613424643828503868, 305623327188018690392981819607012089228265673497

Offset

1,1

Comments

There are 9 forty-eight-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 111603518721165960373027269626940447783074704878, 176512193475025275151977319848516480415708873428, 637711546692957642526533655473763239712353991164, 647866614039059340696936459303056040158682342243, 766803951666578089253935450746129113344740601233) or any number of 9's (for the other four 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. - Clarified by Ray Chandler, Oct 14 2017.

Links

Ray Chandler, Table of n, a(n) for n = 1..9

J. H. E. Cohn, Palindromic differences, Fibonacci Quart. 28 (1990), no. 2, 113-120.

Formula

n = f^9(n), n <> f^k(n) for k < 9, where f: x -> |x - reverse(x)|.

Example

111603518721165960373027269626940447783074704878 -> 766803951666578089253935450746129113344740601233 -> 434697904223266167606880911393148237678581292566 -> 230594281653466673786238177213613424643828503868 -> 637711546692957642526533655473763239712353991164 -> 176512193475025275151977319848516480415708873428 -> 647866614039059340696936459303056040158682342243 -> 305623327188018690392981819607012089228265673497 -> 488753235634961520313936369686084721653457653006 -> 111603518721165960373027269626940447783074704878

Crossrefs

Cf. A072142, A072143, A072718, A072719, A215669, A292634, A292635, A292846, A292856, A292857, A292859.

Sequence in context: A227768 A095486 A095488 * A135956 A095490 A280419

Adjacent sequences: A292855 A292856 A292857 * A292859 A292860 A292861

Keyword

nonn,base

Author

Meritxell Vila Miñana, Sep 25 2017

Extensions

Terms ordered by Ray Chandler, Sep 27 2017

Status

approved