A018252 The nonprime numbers: 1 together with the composite numbers, A002808.

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

1,2

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
(PARI) a(n) = my(k=0); while(-n+n-=k-k=primepi(n), ); n; \\ Ruud H.G. van Tol, Jul 15 2024 (after code in A002808)
(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