A292857 Numbers n such that 8 applications of 'Reverse and Subtract' lead to n, whereas fewer than 8 applications do not lead to n.

16914079504181797053273763831171860502859028, 16914099886383117186009041817970531210859028, 31253512653248719266062943707325665377464777, 31253591994370732566027032487192660079464777

Offset

1,1

Comments

There are 8 forty-four-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 16914079504181797053273763831171860502859028, 46492964703403651468863122584458570244070436, 65181741002635316783463471248546280094182933) or any number of 9's (for the other five 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..8

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

Formula

n = f^8(n), n <> f^k(n) for k < 8, where f: x -> |x - reverse(x)|.

Example

16914079504181797053273763831171860502859028 -> 65181741002635316783463471248546280094182933 -> 31253591994370732566027032487192660079464777 -> 46492905012258445857045034036514689840070436 -> 16914099886383117186009041817970531210859028 -> 65181701327124854628081026353167837688182933 -> 31253512653248719266062943707325665377464777 -> 46492964703403651468863122584458570244070436 -> 16914079504181797053273763831171860502859028

Crossrefs

Cf. A072142, A072143, A072718, A072719, A215669, A292634, A292635, A292846, A292856, A292858, A292859.

Sequence in context: A095478 A291353 A095480 * A121977 A095482 A160678

Adjacent sequences: A292854 A292855 A292856 * A292858 A292859 A292860

Keyword

nonn,base,changed

Author

Meritxell Vila Miñana, Sep 25 2017

Extensions

Terms ordered by Ray Chandler, Sep 27 2017

Status

approved