A141468 Zero together with the nonprime numbers A018252.

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

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 11 2008

Keywords

• nonn

Comments

0 and 1 together with the composite numbers (A002808). - Omar E. Pol, Jul 04 2009

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..17739

Crossrefs

Cf. A018252, A002808, A054546 (first differences).

Programs

Haskell

a141468 n = a141468_list !! (n-1)
a141468_list = 0 : a018252_list  -- Reinhard Zumkeller, May 31 2013

Maple

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

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 *)

PARI

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

PARI

list(lim)=if(lim<1, return(if(lim<0,[],[0]))); my(v=List([0,1])); forcomposite(n=4,lim\1, listput(v,n)); Vec(v) \\ Charles R Greathouse IV, Jul 15 2024

Python

from sympy import composite
def A141468(n): return n-1 if n < 3 else composite(n-2) # Chai Wah Wu, Oct 11 2024

Formula

a(1) = 0; a(n) = A018252(n-1), n > 1. - Omar E. Pol, Aug 13 2009

a(n) = A018252(n) - A054546(n). - Omar E. Pol, Oct 21 2011

a(n) = A002808(n-2) for n > 2 . - Robert G. Wilson v, Jan 29 2015, corrected by Rémi Guillaume, Aug 26 2024.

Extensions

Added 68 by R. J. Mathar, Aug 14 2008

Better definition from Omar E. Pol, Jun 30 2009