A292857 - OEIS

%I #18 Jan 05 2025 19:51:41

%S 16914079504181797053273763831171860502859028,

%T 16914099886383117186009041817970531210859028,

%U 31253512653248719266062943707325665377464777,31253591994370732566027032487192660079464777

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

%C 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.

%H Ray Chandler, <a href="/A292857/b292857.txt">Table of n, a(n) for n = 1..8</a>

%H J. H. E. Cohn, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/28-2/cohn.pdf">Palindromic differences</a>, Fibonacci Quart. 28 (1990), no. 2, 113-120.

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

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

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

%K nonn,base

%O 1,1

%A _Meritxell Vila Miñana_, Sep 25 2017

%E Terms ordered by _Ray Chandler_, Sep 27 2017