Search: id:A018252
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%I A018252
%S A018252 1,4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,
%T A018252 35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,
%U A018252 63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88
%N A018252 The nonprime numbers (1 together with the composite numbers, A002808).
%C A018252 d(n)<>2 (cf. A000005). [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 17 2009]
%C A018252 Number of prime divisors of n (counted with multiplicity)<>1. [From Juri-Stepan 
               Gerasimov (2stepan(AT)rambler.ru), Oct 30 2009]
%C A018252 Largest nonprime<nth composite. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 29 2009]
%C A018252 The nonnegative nonprimes A141468 without zero; the natural nonprimes; 
               the whole nonprimes; the counting nonprimes. If the nonprime numbers 
               A141468 which are also the nonnegative integers A001477, then the 
               nonprimes A141468 also called the nonnegative nonprimes. If the nonprime 
               numbers A018252 which are also the natural (or whole or counting) 
               numbers A000027, then the nonprimes A018252 also called the natural 
               nonprimes, the whole nonprimes and the counting nonprimes. [From 
               Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Nov 22 2009]
%D A018252 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 
               3rd ed., Oxford Univ. Press, 1954, p. 2.
%H A018252 N. J. A. Sloane, <a href="b018252.txt">List of nonprimes up to 20000: 
               Table of n, a(n) for n = 1..17738</a>
%H A018252 Unknown, <a href="http://www.pijnappel2.tmfweb.nl/no_primes.htm">The 
               n-th nonprime</a>.
%H A018252 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MonicaSet.html">Monica Set</a>
%H A018252 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SuzanneSet.html">Suzanne Set</a>
%H A018252 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A018252 Let b(0)=n+pi(n) and b(n+1)=n+pi(b(n)), with pi(n)=A000720(n); then a(n) 
               is the limit value of b(n). - Floor van Lamoen (fvlamoen(AT)hotmail.com), 
               Oct 08 2001
%F A018252 a(n) = A137621(A137624(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jan 30 2008
%p A018252 with(numtheory); sort(convert(convert([ seq(i,i=1..541) ],set) minus 
               convert([ seq(ithprime(i),i=1..100) ],set),list));
%p A018252 seq(`if`(not isprime(n),n,NULL),n=1..88); [From Peter Luschny (peter(AT)luschny.de), 
               Jul 29 2009]
%t A018252 NonPrime[n_Integer] := FixedPoint[n + PrimePi[ # ] &, n + PrimePi[n]]; 
               Table[ NonPrime[n], {n, 1, 75} ]
%o A018252 (MAGMA) [n : n in [1..100] | not IsPrime(n) ];
%o A018252 Contribution from Michael Porter (michael_b_porter(AT)yahoo.com), Nov 
               06 2009: (Start)
%o A018252 (PARI) isA018252(n) = !isprime(n)
%o A018252 A018252(n) = {local(a,b);b=n;a=1;while(a!=b,a=b;b=n+primepi(a));b} (End)
%Y A018252 Cf. A000040, A002808.
%Y A018252 Cf. A000005, A001222. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 30 2009]
%Y A018252 Sequence in context: A133576 A088224 A002808 this_sequence A141468 A077091 
               A051035
%Y A018252 Adjacent sequences: A018249 A018250 A018251 this_sequence A018253 A018254 
               A018255
%K A018252 nonn,nice,easy,core,new
%O A018252 1,2
%A A018252 N. J. A. Sloane (njas(AT)research.att.com).

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