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A006508
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a(n+1) = a(n)-th composite number, with a(0) = 1.
(Formerly M3357)
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20
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1, 4, 9, 16, 26, 39, 56, 78, 106, 141, 184, 236, 299, 374, 465, 570, 696, 843, 1014, 1212, 1441, 1708, 2014, 2365, 2769, 3226, 3749, 4343, 5016, 5774, 6630, 7596, 8676, 9897, 11259, 12784, 14482, 16383, 18502, 20847, 23458, 26354, 29562, 33112, 37041, 41370
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OFFSET
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0,2
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COMMENTS
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Generated by a sieve: start with natural numbers, remove those terms which occupy positions which are prime, leaving 1,4,6,8,9,10,12,14,15,16,18,...; remove those terms whose positions are primes plus one; leaving 1,4,9,12,15,16,18,...; remove those whose positions are primes plus two; continue. - Robert G. Wilson v, Jan 06 2008
Number of terms <= 10^k, k=0..: 1, 3, 8, 18, 34, 54, 80, 110, 147, 188, 235, 287, 345, 407, 475, ..., . - Robert G. Wilson v, Jan 06 2008
The first occurrence of a k-almost prime or 0 if not present: 1, 0, 4, 78, 16, 696, 5016, 95920, 46144, 10236034900, 600374208, 1613472, 21565696412400, 0, 24323590656, ..., . - Robert G. Wilson v, Jan 06 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Popular Computing (Calabasas, CA), Contest 5 Results. Annotated and scanned copy of page PC41-15 of Vol. 4 (No. 41, Aug 1976).
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MATHEMATICA
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Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; NestList[ Composite@# &, 1, 45] (* Labos Elemer *)
With[{c=Select[Range[42000], CompositeQ]}, NestList[c[[#]]&, 1, 45]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 03 2018 *)
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PROG
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(Haskell)
a006508 n = a006508_list !! n
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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