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%I #33 Oct 22 2017 09:51:08
%S 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,
%T 36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,
%U 66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88
%N Zero together with the nonprime numbers A018252.
%C 0 and 1 together with the composite numbers (A002808). [_Omar E. Pol_, Jul 04 2009]
%C A141468 U A000040 = A001477 = A158611 U A002808. [_Juri-Stepan Gerasimov_, Jul 28 2009, Sep 27 2009]
%C 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
%C 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]
%C Numbers n such that n-th prime*n is not semiprime. [_Juri-Stepan Gerasimov_, Sep 27 2010]
%C The nonnegative numbers that are not primes. First differences give A054546. - _Omar E. Pol_, Oct 21 2011
%C 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
%H N. J. A. Sloane, <a href="/A141468/b141468.txt">Table of n, a(n) for n = 1..17739</a>
%F a(1) = 0. a(n) = A018252(n-1), n > 1. - _Omar E. Pol_, Aug 13 2009
%F a(n) = A018252(n) - A054546(n). - _Omar E. Pol_, Oct 21 2011
%F a(n) = A018252(n+1) = A002808(n+2) for n>1. - _Robert G. Wilson v_, Jan 29 2015
%p 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
%t nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; Array[ nonPrime, 66, 0] (* _Robert G. Wilson v_, Jan 29 2015 *)
%t Join[{0,1},Select[Range[100],CompositeQ]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 22 2017 *)
%o (Haskell)
%o a141468 n = a141468_list !! (n-1)
%o a141468_list = 0 : a018252_list -- _Reinhard Zumkeller_, May 31 2013
%Y Cf. A018252, A002808.
%K nonn
%O 1,3
%A _Juri-Stepan Gerasimov_, Aug 11 2008
%E Added 68 by _R. J. Mathar_, Aug 14 2008
%E Better definition from _Omar E. Pol_, Jun 30 2009
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