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

1,2

Links

Table of n, a(n) for n=1..29.

Example

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.

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

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.

Sequence in context: A013646 A059800 A330293 * A280893 A215508 A215385

Adjacent sequences: A302684 A302685 A302686 * A302688 A302689 A302690

Keyword

nonn,base

Author

Daniel Sterman, Apr 11 2018

Extensions

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

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

Status

approved