A249398 Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n-1),a(n)).

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 15625, 20000, 25000, 31250, 40000, 50000, 62500, 78125, 100000, 125000, 156250, 200000, 250000, 312500, 390625, 500000, 625000, 781250, 1000000

Offset: 1

Author

Paolo P. Lava, Dec 01 2014

Keywords

• nonn
• base

Examples

			a(1) = 1;
a(2) = 2 -> 12 /2 = 6;
Now we cannot use 3 as the next term because it does not divide 23.
a(3) = 4 -> 24 / 4 = 6;
a(4) = 5 -> 45 / 5 = 9;
Again, 6, 7, 8 and 9 cannot be used as the next term.
a(5) = 10 -> 510 / 10 = 51;
a(6) = 20 -> 1020 / 20 = 51;
a(7) = 25 -> 2025 / 25 = 81; etc.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A171785, A249399, A250745, A250746, A250747.

Programs

Maple

with(numtheory); P:=proc(q) local a,k,n; print(1); a:=1;
for n from 2 to q do if type((a*10^(1+ilog10(n))+n)/n,integer)
then a:=n; print(n); fi; od; end: P(10^12);