cp's OEIS Frontend

A383230 Numbers k whose decimal representation can be split in three parts which can be used as seeds for a tribonacci-like sequence containing k itself.

%I A383230 #46 May 23 2025 20:02:39
%S A383230 197,742,1007,1257,1484,1749,1789,3241,4349,4515,4851,5709,6482,6925,
%T A383230 7756,8196,8449,8698,10232,10997,11627,16898,17206,18353,19789,20464,
%U A383230 27315,30696,31385,35537,40928,43367,44111,48310,48591,49228,50574,58506,62770,79976,88222
%N A383230 Numbers k whose decimal representation can be split in three parts which can be used as seeds for a tribonacci-like sequence containing k itself.
%C A383230 There are 306 terms < 10^8.
%C A383230 If the number k is rewritten as the concatenation of a, b and c, the problem is to find an integer x such that k = a*A000073(x) + b*A001590(x+1) + c*A000073(x+1).
%C A383230 Is there any term that results from more than one concatenation?
%H A383230 David A. Corneth, <a href="/A383230/b383230.txt">Table of n, a(n) for n = 1..965</a> (first 306 terms from Paolo P. Lava, terms <= 10^11)
%H A383230 Paolo P. Lava, <a href="/A383230/a383230.pdf">List of tribonacci-like sequences</a>
%e A383230 1007 can be split into 10, 0, 7 and the tribonacci-like sequence contains 1007 itself: 10, 0, 7, 17, 24, 48, 89, 161, 298, 548, 1007 ... (x = 9, as per second comment);
%e A383230 1257 can be split into 1, 25, 7 and the tribonacci-like sequence contains 1257 itself: 1, 25, 7, 33, 65, 105, 203, 373, 681, 1257 ... (x = 8, as per second comment);
%e A383230 16898 can be split into 16, 8, 98 and the tribonacci-like sequence contains 16898 itself: 16, 8, 98, 122, 228, 448, 798, 1474, 2720, 4992, 9186, 16898 ... (x = 10, as per second comment).
%p A383230 P:=proc(q) local b,c,d,f1,f2,f3,i,j,m,n,t,v,y,x,w; i:=[]; for n from 100 to q do b:=length(n);
%p A383230 for t from 1 to b-2 do c:=n mod 10^t; m:=trunc(n/10^t); d:=length(m);
%p A383230 for j from 1 to d-1 do x:=trunc(m/10^j); y:=m mod 10^j; f1:=2; f2:=3; f3:=4; v:=x*f1+y*f2+c*f3;
%p A383230 while v<n do w:=f3; f3:=f2+f3; f2:=f1+w; f1:=w; v:=x*f1+y*f2+c*f3; od;
%p A383230 if v=n then i:=[op(i),n]; break; fi; od; od; od; op(i); end: P(10^5);
%Y A383230 Cf. A000073, A000213, A001590, A007629, A130792.
%K A383230 nonn,base
%O A383230 1,1
%A A383230 _Paolo P. Lava_, Apr 20 2025