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A006508 a(n+1) = a(n)-th composite number, with a(0) = 1.
(Formerly M3357)
19

%I M3357

%S 1,4,9,16,26,39,56,78,106,141,184,236,299,374,465,570,696,843,1014,

%T 1212,1441,1708,2014,2365,2769,3226,3749,4343,5016,5774,6630,7596,

%U 8676,9897,11259,12784,14482,16383,18502,20847,23458,26354,29562,33112,37041,41370

%N a(n+1) = a(n)-th composite number, with a(0) = 1.

%C 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

%C 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

%C 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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Chai Wah Wu, <a href="/A006508/b006508.txt">Table of n, a(n) for n = 0..900</a> (n = 0..503 from Robert G. Wilson v)

%H Popular Computing (Calabasas, CA), <a href="/A006508/a006508.png">Contest 5 Results</a>. Annotated and scanned copy of page PC41-15 of Vol. 4 (No. 41, Aug 1976).

%H <a href="/index/Si#sieve">Index entries for sequences generated by sieves</a>

%t Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; NestList[ Composite@# &, 1, 45] (* _Labos Elemer_ *)

%t With[{c=Select[Range[42000],CompositeQ]},NestList[c[[#]]&,1,45]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 03 2018 *)

%o (Haskell)

%o a006508 n = a006508_list !! n

%o a006508_list = iterate a002808 1 -- _Reinhard Zumkeller_, Oct 24 2011

%Y Cf. A007097, A002808.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _Robert G. Wilson v_, Jan 06 2008

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)