A141468 Zero together with the nonprime numbers A018252.

0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88

Offset

1,3

Comments

0 and 1 together with the composite numbers (A002808). [Omar E. Pol, Jul 04 2009]

A141468 U A000040 = A001477 = A158611 U A002808. [Juri-Stepan Gerasimov, Jul 28 2009, Sep 27 2009]

The sequence of nonprime numbers (A018252) starts: 1, 4, 6, 8, 9, 10, 12, 14, 15,... (Offset=1). Note that zero is not a member of A018252 because the words "prime" and "nonprime" normally refer to the natural numbers or positive integers (1,2,3,4,5,6,...). We know that the n-th nonprime is A018252(n). Then, about this sequence (A141468 with offset=1), we can write: A141468(n+1) = A018252(n), (See example and formula). - Omar E. Pol, Aug 13 2009

The nonnegative nonprimes. If nonprime numbers A141468 which are also the nonnegative integers, then the nonprimes A141468 also called the nonnegative nonprimes and the nonprimes A018252 also called the natural nonprimes, the whole nonprimes, the counting nonprimes. [Juri-Stepan Gerasimov, Nov 22 2009]

Numbers n such that n-th prime*n is not semiprime. [Juri-Stepan Gerasimov, Sep 27 2010]

The nonnegative numbers that are not primes. First differences give A054546. - Omar E. Pol, Oct 21 2011

There are a large number of sequences in the OEIS in which is written that a(n) is the n-th nonprime, which is wrong. The n-th nonprime is A018252(n). See formulas. - Omar E. Pol, Oct 21 2011

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..17739

Formula

a(1) = 0. a(n) = A018252(n-1), n > 1. - Omar E. Pol, Aug 13 2009

a(n) = A018252(n) - A054546(n). - Omar E. Pol, Oct 21 2011

a(n) = A018252(n+1) = A002808(n+2) for n>1. - Robert G. Wilson v, Jan 29 2015

Maple

A141468 := proc(n) option remember; local a; if n <=2 then n-1 ; else for a from procname(n-1)+1 do if not isprime(a) then return a; end if; end do; end if; end proc: # R. J. Mathar, Dec 13 2010

Mathematica

nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; Array[ nonPrime, 66, 0] (* Robert G. Wilson v, Jan 29 2015 *)
Join[{0, 1}, Select[Range[100], CompositeQ]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 22 2017 *)

Prog

(Haskell)
a141468 n = a141468_list !! (n-1)
a141468_list = 0 : a018252_list  -- Reinhard Zumkeller, May 31 2013

Crossrefs

Cf. A018252, A002808.

Sequence in context: A088224 A002808 A018252 * A140347 A140209 A077091

Adjacent sequences: A141465 A141466 A141467 * A141469 A141470 A141471

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 11 2008

Extensions

Added 68 by R. J. Mathar, Aug 14 2008

Better definition from Omar E. Pol, Jun 30 2009

Status

approved