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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).

Index entries for sequences generated by sieves

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

N. J. A. Sloane

EXTENSIONS

Edited by Robert G. Wilson v, Jan 06 2008

STATUS

approved

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Last modified February 19 18:51 EST 2019. Contains 320328 sequences. (Running on oeis4.)