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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. 7
1, 2, 3, 41, 7, 9, 137131, 61, 2023244487101, 13, 19, 11, 143, 142733, 21, 17, 193, 37, 3907, 1290366811360047359, 1805030483980039, 3803623, 233, 31, 16734859281232450924683549622800460252243870584270124214740588592572109094249481762247353040452919 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..25.

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: A077336 A242174 A288519 * A013646 A059800 A302687

Adjacent sequences:  A240585 A240586 A240587 * A240589 A240590 A240591

KEYWORD

nonn,base,more

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

STATUS

approved

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Last modified September 15 04:06 EDT 2019. Contains 327062 sequences. (Running on oeis4.)