

A141468


Zero together with the nonprime numbers A018252.


202



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
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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. [JuriStepan 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 nth 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. [JuriStepan Gerasimov, Nov 22 2009]
Numbers n such that nth prime*n is not semiprime. [JuriStepan 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 nth nonprime, which is wrong. The nth 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(n1), 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 n1 ; else for a from procname(n1)+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 !! (n1)
a141468_list = 0 : a018252_list  Reinhard Zumkeller, May 31 2013


CROSSREFS

Cf. A018252, A002808.
Sequence in context: A088224 A002808 A018252 * A140209 A140347 A077091
Adjacent sequences: A141465 A141466 A141467 * A141469 A141470 A141471


KEYWORD

nonn


AUTHOR

JuriStepan 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



