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A111269
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Smallest divisor of n-th composite number (A002808(n)) which has not occurred earlier in the sequence.
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2
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1, 2, 4, 3, 5, 6, 7, 15, 8, 9, 10, 21, 11, 12, 25, 13, 27, 14, 30, 16, 33, 17, 35, 18, 19, 39, 20, 42, 22, 45, 23, 24, 49, 50, 51, 26, 54, 55, 28, 57, 29, 60, 31, 63, 32, 65, 66, 34, 69, 70, 36, 37, 75, 38, 77, 78, 40, 81, 41, 84, 85, 43, 87, 44, 90, 91, 46, 93, 47, 95, 48, 98, 99
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OFFSET
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1,2
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COMMENTS
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A permutation of the natural numbers. Subsidiary sequence: k :a(k) = k.
This sequence is a permutation of the positive integers. - Leroy Quet, Feb 03 2007
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LINKS
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EXAMPLE
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Smallest divisor of the n-th composite number not already in the sequence.
The 7th composite integer is 14. The divisors of 14 are 1,2,7,14. Of these, 1 and 2 occur among the first 6 terms of the sequence. So 7 is the lowest divisor of 14 which is missing from the first 6 terms of the sequence. Therefore a(7) = 7. - Leroy Quet, Feb 03 2007
The 13th composite number is 22. Its divisors are {1, 2, 11, 22}. 1 and 2 are already in the sequence. The smallest divisor of 22 which is not already in the sequence is 11. So a(13)=11. - Diana L. Mecum, Jan 03 2009
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MAPLE
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N:= 200: # to get up to a(m), where m is the number of composites <= N
Comps:= {$2..N} minus select(isprime, {2, seq(2*i+1, i=1..floor((N-1)/2))}):
S:= {}:
for n from 1 to nops(Comps) do
A[n]:= min(numtheory:-divisors(Comps[n]) minus S);
S:= S union {A[n]}
od:
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MATHEMATICA
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f[l_List] := Block[{n = Length[l] + 1, c = 1, k = n}, While[k > 0, c++; While[PrimeQ[c], c++]; k--; ]; Append[l, First[Select[Divisors[c], FreeQ[l, #] &]]]]; Nest[f, {}, 10000] (* Ray Chandler, Feb 07 2007 *)
CompositeList = Drop[Complement[Range[2741], Prime[Range[400]]], 1]; sequence = {1, 2, 4, 3}; Do[AppendTo[sequence, DeleteCases[Table[If[! MemberQ[sequence, Divisors[CompositeList[[n]]][[j]]], Divisors[CompositeList[[n]]][[j]], ], {j, 1, Length[Divisors[CompositeList[[n]]]]}], Null][[1]]], {n, 5, 1000}]; sequence (* Diana L. Mecum, Jul 21 2012 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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Added terms a(23) - a(999) - Diana L. Mecum, Jan 03 2009, corrected Jul 21 2012
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STATUS
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approved
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