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.

197, 742, 1007, 1257, 1484, 1749, 1789, 3241, 4349, 4515, 4851, 5709, 6482, 6925, 7756, 8196, 8449, 8698, 10232, 10997, 11627, 16898, 17206, 18353, 19789, 20464, 27315, 30696, 31385, 35537, 40928, 43367, 44111, 48310, 48591, 49228, 50574, 58506, 62770, 79976, 88222

Offset: 1

Author

Paolo P. Lava, Apr 20 2025

Keywords

• nonn
• base

Comments

There are 306 terms < 10^8.

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).

Is there any term that results from more than one concatenation?

Examples

			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);
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);
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).
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..965 (first 306 terms from Paolo P. Lava, terms <= 10^11)
• Paolo P. Lava, List of tribonacci-like sequences

Crossrefs

Cf. A000073, A000213, A001590, A007629, A130792.

Programs

Maple

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);
for t from 1 to b-2 do c:=n mod 10^t; m:=trunc(n/10^t); d:=length(m);
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;
while v