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 A018252 The nonprime numbers: 1 together with the composite numbers, A002808. 376
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 OFFSET 1,2 COMMENTS d(a(n)) != 2 (cf. A000005). - Juri-Stepan Gerasimov, Oct 17 2009 Number of prime divisors of a(n) (counted with multiplicity) != 1. - Juri-Stepan Gerasimov, Oct 30 2009 Largest nonprime < n-th composite. - Juri-Stepan Gerasimov, Oct 29 2009 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. - Juri-Stepan Gerasimov, Nov 22 2009 Smallest nonprime > n-th nonnegative nonprime. - Juri-Stepan Gerasimov, Dec 04 2009 a(n) = A175944(A014284(n)) = A175944(A175965(n)). - Reinhard Zumkeller, Mar 18 2011 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 2. LINKS N. J. A. Sloane, List of nonprimes up to 20000: Table of n, a(n) for n = 1..17738 Eric Weisstein's World of Mathematics, Monica Set Eric Weisstein's World of Mathematics, Suzanne Set Index entries for "core" sequences FORMULA 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, Oct 08 2001 a(n) = A137621(A137624(n)). - Reinhard Zumkeller, Jan 30 2008 A010051(a(n)) = 0. - Reinhard Zumkeller, Mar 31 2014 A239968(a(n)) = n. - Reinhard Zumkeller, Dec 02 2014 MAPLE with(numtheory); sort(convert(convert([ seq(i, i=1..541) ], set) minus convert([ seq(ithprime(i), i=1..100) ], set), list)); seq(`if`(not isprime(n), n, NULL), n=1..88); # Peter Luschny, Jul 29 2009 A018252 := proc(n) option remember; if n = 1 then 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, Oct 22 2010 MATHEMATICA nonPrime[n_Integer] := FixedPoint[n + PrimePi@# &, n + PrimePi@ n]; Array[ nonPrime, 75] (* Robert G. Wilson v, Jan 29 2015, based on the algorithm by Labos Elemer in A006508 *) max = 90; Complement[Range[max], Prime[Range[PrimePi[max]]]] (* Harvey P. Dale, Aug 12 2011 *) Join[{1}, Select[Range[100], CompositeQ]] (* Jean-François Alcover, Nov 07 2021 *) PROG (Magma) [n : n in [1..100] | not IsPrime(n) ]; (PARI) isA018252(n) = !isprime(n) A018252(n) = {local(a, b); b=n; a=1; while(a!=b, a=b; b=n+primepi(a)); b} \\ Michael B. Porter, Nov 06 2009 (Sage) def A018252_list(n) : return [k for k in (1..n) if not k.is_prime()] A018252_list(88) # Peter Luschny, Feb 03 2012 (Haskell) a018252 n = a018252_list !! (n-1) a018252_list = filter ((== 0) . a010051) [1..] -- Reinhard Zumkeller, Mar 31 2014 (GAP) A018252 := Difference([1..10^5], Filtered([1..10^5], IsPrime)); # Muniru A Asiru, Oct 21 2017 (Python) from sympy import isprime def ok(n): return not isprime(n) print([k for k in range(1, 89) if ok(k)]) # Michael S. Branicky, Nov 10 2022 (Python) from sympy import composite def A018252(n): return 1 if n == 1 else composite(n-1) # Chai Wah Wu, Nov 15 2022 CROSSREFS Cf. A000040 (complement), A002808. Cf. A000005, A001222, A141468. Boustrophedon transforms: A230955, A230954. Cf. A010051, A239968. Sequence in context: A192607 A088224 A002808 * A141468 A140347 A140209 Adjacent sequences: A018249 A018250 A018251 * A018253 A018254 A018255 KEYWORD nonn,nice,easy,core AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 28 02:54 EDT 2023. Contains 365714 sequences. (Running on oeis4.)