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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).
• Index entries for sequences generated by sieves

Crossrefs

Cf. A007097, A002808.

Programs

Haskell

a006508 n = a006508_list !! n
a006508_list = iterate a002808 1  -- Reinhard Zumkeller, Oct 24 2011

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 *)

Extensions

Edited by Robert G. Wilson v, Jan 06 2008