cp's OEIS Frontend

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.

A307863 Numbers x = concat(a,b) such that b and a are the first two terms for a Fibonacci-like sequence containing x itself.

Original entry on oeis.org

17, 21, 25, 42, 63, 84, 105, 123, 126, 147, 168, 189, 197, 246, 295, 369, 492, 787, 1033, 1115, 1141, 1248, 1279, 1997, 2066, 2230, 2282, 2496, 2995, 3099, 3345, 3423, 3744, 4460, 4564, 4992, 5411, 5575, 5705, 6690, 6846, 7987, 10112, 10483, 10822, 11059, 11107
Offset: 1

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Author

Paolo P. Lava, May 02 2019

Keywords

Comments

Similar to A130792 but here the sums start b + a = c, a + c = d, etc.
First six terms are also the first six Inrepfigit numbers (A128546).
Being x = concat(a,b), the problem is to find an index y such that x = b*F(y) + a*F(y+1), where F(y) is a Fibonacci number (see file with values of x, b, a, y, for 1< x <10^6, in Links). All the listed numbers admit only one unique concatenation that, through the addition process, leads to themselves. Is there any number that admits more than one single concatenation?

Examples

			123 can be split into 1 and 23 and the Fibonacci-like sequence: 23, 1, 24, 25, 49, 74, 123, ... contains 123 itself.
		

Crossrefs

Programs

  • Maple
    P:=proc(n) local j,t,v; v:=array(1..100);
    for j from 1 to length(n)-1 do v[1]:=n mod 10^j; v[2]:=trunc(n/10^j);
    v[3]:=v[1]+v[2]; t:=3; while v[t]Paolo P. Lava, May 02 2019