This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A130792 #36 Apr 18 2025 20:10:09
%S A130792 14,19,28,47,61,75,122,149,183,199,244,298,305,323,366,427,488,497,
%T A130792 549,646,795,911,969,1292,1301,1499,1822,1999,2087,2602,2733,2998,
%U A130792 3089,3248,3379,3644,3903,4555,4997,5204,5466,6178,6377,6496,6505,7288,7806,7995
%N A130792 Numbers k whose representation can be split in two parts which can be used as seeds for a Fibonacci-like sequence containing k itself.
%C A130792 The 6 terms with two digits are also Keith numbers. There are 233 numbers below 10^6 in this sequence.
%C A130792 Contribution from _Paolo P. Lava_, Apr 18 2025: (Start)
%C A130792 If the number k is rewritten as the concatenation of a and b, the problem is to find an integer x such that k = a*F(x) + b*F(x+1), where F(x) is a Fibonacci number (see in Links file with values of k, a, b, x, for k<10^6).
%C A130792 All the listed numbers admit only one concatenation that, through the addition process, leads to themselves. Is there any number that admits more than one single concatenation?
%C A130792 Sequence is infinite. Let us consider the numbers 19, 199, 1999, 19...9 and let us divide them as (1, 9), (1, 99), (1, 999), (1, 9...9). In two steps we have the initial numbers back: 1 + 9 = 10 and 9 + 10 = 19; 1 + 99 = 100 and 99 + 100 = 199, etc. (End)
%H A130792 Michel Marcus, <a href="/A130792/b130792.txt">Table of n, a(n) for n = 1..406</a> (first 200 terms from Paolo Lava)
%H A130792 Paolo P. Lava, <a href="/A130792/a130792.pdf">List of k, a, b, x</a>
%e A130792 122 can be split into 12 and 2 and the Fibonacci-like sequence: 12, 2, 14, 16, 30, 46, 76, 122, ... contains 122 itself.
%t A130792 testQ[n_]:= Block[{x, y, z, p = 10, r = False}, While[p < n, x = Floor[n/p]; y = Mod[n, p]; While[y < n, z = x + y; x = y; y = z]; If[y == n, r = True; Break[]]; p *= 10]; r]; Select[Range[10^4],testQ]
%o A130792 (PARI) isok(n) = {nb = #Str(n); for (i=1, nb-1, x = n\10^i; y = n - 10^i*x; ok = 0; while(!ok, z = x + y; if (z > n, ok = 1); if (z == n, return (1)); x = y; y = z;));} \\ _Michel Marcus_, Oct 08 2014
%Y A130792 Cf. A007629.
%K A130792 base,nonn
%O A130792 1,1
%A A130792 _Giovanni Resta_, Aug 20 2007