A302687 a(1) = 1; a(2) = 2; then a(n) is the smallest number > a(n-1) such that a(n) divides concat(a(1), a(2), ..., a(n-1)).

1, 2, 3, 41, 43, 129, 9567001, 21147541, 22662659, 23817877, 24837187, 28850377, 28872229, 37916473, 48749751, 70416307, 439229167, 834385607, 2270365163, 2278377431, 3751789547, 4433933101, 4810754611, 14432263833, 15632412757, 30530543651, 42441819717, 65591903199, 65857498407

Offset: 1

Author

Daniel Sterman, Apr 11 2018

Keywords

• nonn
• base

Examples

			a(3) = 3, which makes the concatenation of the first three terms: 123. After 3, the next-highest factor of 123 is 41, so a(4) = 41. The concatenation of the first four terms is then 12341. After 41, the next-highest factor of 12341 is 43, so a(5) = 43.
		

Crossrefs

Compare A240588, in which each term does not need to strictly increase as long as it has not yet appeared in the sequence.

Compare also A171785, in which each term must divide the concatenation of all terms in the sequence including itself.

In A029455, each term divides the concatenation of all smaller positive integers.

In A110740, each term divides the concatenation of all strictly smaller positive integers.

Programs

Maple

A[1]:= 1: A[2]:= 2: C:= 1:
for n from 3 to 20 do
  C:= A[n-1]+C*10^(ilog10(A[n-1])+1);
  A[n]:= min(select(`>`,numtheory:-divisors(C),A[n-1]))
od:
seq(A[i],i=1..20); # Robert Israel, Apr 12 2018

Extensions

a(16)-a(20) from Robert Israel, Apr 12 2018

a(21)-a(29) from Daniel Suteu, Apr 12 2018