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A097060 Revrepfigits (reverse replicating Fibonacci-like digits): Numbers k whose reversal occurs in a sequence generated by starting with the k digits of a number and then continuing the sequence with a number that is the sum of the previous k terms.

%I A097060 #19 Feb 16 2025 08:32:54
%S A097060 12,24,36,48,52,71,341,682,1285,5532,8166,17593,28421,74733,90711,
%T A097060 759664,901921,1593583,4808691,6615651,6738984,8366363,8422611,
%U A097060 26435142,54734431,57133931,79112422,89681171,351247542,428899438,489044741,578989902
%N A097060 Revrepfigits (reverse replicating Fibonacci-like digits): Numbers k whose reversal occurs in a sequence generated by starting with the k digits of a number and then continuing the sequence with a number that is the sum of the previous k terms.
%C A097060 Numbers ending in zero are not permitted since the zeros are dropped upon reversal. However, terms with internal zeros such as 90711 are permitted. Conjectures: 1. Sequence is infinite. 2. Revrepfigits are more rare than repfigits.
%C A097060 There are no 12-digit revrepfigits.
%D A097060 J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 11-13. ASIN: B002ACVZ6O [From _Jason Earls_, Nov 21 2009]
%H A097060 Bernardo Boncompagni and Anton Vrba, <a href="/A097060/b097060.txt">Table of n, a(n) for n = 1..59</a>
%H A097060 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_384.htm">Primepuzzles.net Puzzle 384</a>
%H A097060 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KeithNumber.html">Keith Number</a>
%e A097060 8166 is in the sequence since the sequence 8,1,6,6,21,34,67,128,250, 479,924,1781,3434,6618,..., contains the reversal of 8166.
%t A097060 rKeithQ[n_Integer] := Module[{b = IntegerDigits[n], r, s, k = 0}, If[Mod[n, 10] == 0, False, r = FromDigits[Reverse[b]]; s = Total[b]; While[s < r, AppendTo[b, s]; k++; s = 2*s - b[[k]]]; s == r]]; Select[Range[10, 100000], rKeithQ] (* _T. D. Noe_, Mar 15 2011 *)
%Y A097060 Cf. A007629.
%Y A097060 Cf. A128546 (reverse of these numbers).
%K A097060 base,nonn
%O A097060 1,1
%A A097060 _Jason Earls_, Sep 15 2004
%E A097060 More terms from _Bernardo Boncompagni_ and Anton Vrba (antonvrba(AT)yahoo.com), Jan 05 2007