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.

This page as a plain text file.
%I A307863 #15 May 28 2019 04:26:12
%S A307863 17,21,25,42,63,84,105,123,126,147,168,189,197,246,295,369,492,787,
%T A307863 1033,1115,1141,1248,1279,1997,2066,2230,2282,2496,2995,3099,3345,
%U A307863 3423,3744,4460,4564,4992,5411,5575,5705,6690,6846,7987,10112,10483,10822,11059,11107
%N A307863 Numbers x = concat(a,b) such that b and a are the first two terms for a Fibonacci-like sequence containing x itself.
%C A307863 Similar to A130792 but here the sums start b + a = c, a + c = d, etc.
%C A307863 First six terms are also the first six Inrepfigit numbers (A128546).
%C A307863 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?
%H A307863 Giovanni Resta, <a href="/A307863/b307863.txt">Table of n, a(n) for n = 1..900</a>
%H A307863 Paolo P. Lava, <a href="/A307863/a307863.txt">Values of x, b, a, y, for 1< x <10^6</a>
%e A307863 123 can be split into 1 and 23 and the Fibonacci-like sequence: 23, 1, 24, 25, 49, 74, 123, ... contains 123 itself.
%p A307863 P:=proc(n) local j,t,v; v:=array(1..100);
%p A307863 for j from 1 to length(n)-1 do v[1]:=n mod 10^j; v[2]:=trunc(n/10^j);
%p A307863 v[3]:=v[1]+v[2]; t:=3; while v[t]<n do t:=t+1; v[t]:=v[t-2]+v[t-1]; od;
%p A307863 if v[t]=n then RETURN(n); break; fi; od; end: seq(P(i),i=1..11107); # _Paolo P. Lava_, May 02 2019
%Y A307863 Cf. A128546, A130792, A289868.
%K A307863 nonn,base
%O A307863 1,1
%A A307863 _Paolo P. Lava_, May 02 2019