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 A006508 a(n+1) = a(n)-th composite number, with a(0) = 1. (Formerly M3357) 18
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Chai Wah Wu, Table of n, a(n) for n = 0..900 (n = 0..503 from Robert G. Wilson v) Popular Computing (Calabasas, CA), Contest 5 Results. Annotated and scanned copy of page PC41-15 of Vol. 4 (No. 41, Aug 1976). MATHEMATICA 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 *) PROG (Haskell) a006508 n = a006508_list !! n a006508_list = iterate a002808 1  -- Reinhard Zumkeller, Oct 24 2011 CROSSREFS Cf. A007097, A002808. Sequence in context: A022334 A073171 A049739 * A299898 A009875 A265044 Adjacent sequences:  A006505 A006506 A006507 * A006509 A006510 A006511 KEYWORD nonn,easy AUTHOR EXTENSIONS Edited by Robert G. Wilson v, Jan 06 2008 STATUS approved

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Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)