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A240588
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a(1) = 1, a(2) = 2; for n >= 3, a(n) = least number not included earlier that divides the concatenation of all previous terms.
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11
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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
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OFFSET
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1,2
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COMMENTS
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The next unknown term a(131) requires the factorization of a 517-digit composite number 46297...2963. (End)
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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a = {1, 2}; While[Length[a] < 22,
n = ToExpression[StringJoin[ToString /@ a]];
AppendTo[a, SelectFirst[Sort[Divisors[n]], FreeQ[a, #] &]]
]; a
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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