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.

12, 24, 36, 48, 52, 71, 341, 682, 1285, 5532, 8166, 17593, 28421, 74733, 90711, 759664, 901921, 1593583, 4808691, 6615651, 6738984, 8366363, 8422611, 26435142, 54734431, 57133931, 79112422, 89681171, 351247542, 428899438, 489044741, 578989902

Offset: 1

Author

Jason Earls, Sep 15 2004

Keywords

• base
• nonn

Comments

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.

There are no 12-digit revrepfigits.

Examples

			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.
		

References

• J. Earls, Mathematical Bliss, Pleroma Publications, 2009, pages 11-13. ASIN: B002ACVZ6O [From Jason Earls, Nov 21 2009]

Links

• Bernardo Boncompagni and Anton Vrba, Table of n, a(n) for n = 1..59
• Carlos Rivera, Primepuzzles.net Puzzle 384
• Eric Weisstein's World of Mathematics, Keith Number

Crossrefs

Cf. A007629.

Cf. A128546 (reverse of these numbers).

Programs

Mathematica

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 *)

Extensions

More terms from Bernardo Boncompagni and Anton Vrba (antonvrba(AT)yahoo.com), Jan 05 2007