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

1,2

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)

Links

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

Example

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.

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

Crossrefs

Cf. A096097, A096098, A241811.

Sequence in context: A242174 A340394 A288519 * A013646 A059800 A330293

Adjacent sequences: A240585 A240586 A240587 * A240589 A240590 A240591

Keyword

nonn,base

Author

Paolo P. Lava, Apr 29 2014

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

Status

approved