A240588 a(1) = 1, a(2) = 2; for n >= 3, a(n) = least number not included earlier that divides the concatenation of all previous terms.

1, 2, 3, 41, 7, 9, 137131, 61, 2023244487101, 13, 19, 11, 143, 142733, 21, 17, 193, 37, 3907, 1290366811360047359, 1805030483980039, 3803623, 123, 369, 27, 23, 58271, 47609, 523, 79, 307, 179, 73, 57, 18032419296851, 29, 31, 3281881401611107, 69, 171, 60244474373, 197, 97

Offset: 1

Author

Paolo P. Lava, Apr 29 2014

Keywords

• nonn
• base

Comments

From Scott R. Shannon, Dec 19 2019: (Start)

The next unknown term a(131) requires the factorization of a 517-digit composite number 46297...2963. (End)

Examples

			a(1)=1 and a(2)=2. a(1) U a(2) = 12 and its divisors are 1, 2, 3, 4, 6, 12. Therefore 3 is the least number not yet present in the sequence which divides 12. Again, a(1) U a(2) U a(3) = 123 and its divisors are 1, 3, 41, 123. Therefore a(4)=41. Etc.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..130.

Crossrefs

Cf. A096097, A096098, A241811.

Programs

Maple

with(numtheory):
T:=proc(t) local x, y; x:=t; y:=0; while x>0 do x:=trunc(x/10); y:=y+1; od; end:
P:=proc(q) local a,b,c,k,n; b:=12; print(1); print(2); c:=[1,2];
for n from 1 to q do a:=sort([op(divisors(b))]); for k from 2 to nops(a) do
if not member(a[k],c) then c:=[op(c),a[k]]; b:=a[k]+b*10^T(a[k]); print(a[k]); break;
fi; od; od; end: P(19);

Mathematica

a = {1, 2}; While[Length[a] < 22,
  n = ToExpression[StringJoin[ToString /@ a]];
  AppendTo[a, SelectFirst[Sort[Divisors[n]], FreeQ[a, #] &]]
]; a

Extensions

a(20)-a(40) from Alois P. Heinz, May 08 2014

a(22) corrected by Ryan Hitchman, Sep 14 2017

a(23)-a(25) from Robert Price, May 16 2019

a(23)-a(25) corrected, and a(26)-a(43) added by Scott R. Shannon, Dec 10 2019