A265737 Consider any concatenation of the type n = concat(a,b). Sequence lists numbers that are the sum of the products of some of such couples a and b.

655, 1064, 1258, 1461, 1642, 2361, 2464, 3382, 3442, 3835, 4738, 4925, 5275, 6208, 6550, 8291, 9274, 10640, 11197, 11548, 11593, 12508, 12580, 12915, 13706, 14610, 16420, 16625, 17184, 18232, 19641, 23610, 24640, 31714, 33820, 34420, 36226, 38350, 39826, 40722

Offset: 1

Author

Paolo P. Lava, Dec 15 2015

Keywords

• nonn
• base

Comments

In the first 1000 terms the primes are 8291, 11197, 11593, 72253, 315521, 1514917, 2593361, 10154231, 15878617, 17209327, 22146101, 50828863, 53107111, 67328713, 120543559, 151134019.

Any number of the forms concat(125^z, x, 8^z, y) and concat(160, x, 625, y), where x and y are k and j zeros, with k,j>=0, and z = {1, 2, 3} is part of the sequence.

n is in the sequence, iff 10*n is. So the first term of sequence which is divisible by 10^n is 655*10^n. - Altug Alkan, Dec 17 2015

Examples

			For 655 we have: 6 * 55 = 320, 65 * 5 = 325 and 320 + 325 = 665.
For 1064 we have: 10 * 64 = 640, 106 * 4 = 424 and 640 + 424 = 1064.
For 41464 we have: 4 * 1464 = 5856, 41 * 464 = 19024, 4146 * 4 =  16584 and 5856 + 19024 + 16584 = 41464.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065759.

Programs

Maple

with(combinat): P:=proc(q) local a,j,k,n; for n from 1 to q do a:={};
for k from 1 to ilog10(n) do a:=a union {(n mod 10^k)*trunc(n/10^k)}; od; a:=choose(a);
for k from 2 to nops(a) do if n=add(a[k][j],j=1..nops(a[k])) then print(n); break; fi; od;
od; end: P(10^9);