A129768 Number of odd nonprime numbers less than the n-th prime.

1, 1, 1, 1, 2, 2, 3, 3, 4, 6, 6, 8, 9, 9, 10, 12, 14, 14, 16, 17, 17, 19, 20, 22, 25, 26, 26, 27, 27, 28, 34, 35, 37, 37, 41, 41, 43, 45, 46, 48, 50, 50, 54, 54, 55, 55, 60, 65, 66, 66, 67, 69, 69, 73, 75, 77, 79, 79, 81, 82, 82, 86, 92, 93, 93, 94, 100, 102, 106, 106, 107, 109

Offset: 1

Author

Giovanni Teofilatto, May 16 2007

Keywords

• nonn

Comments

Also, a(n)=sum_{k=n-th even number..n-th odd prime together with 1}-k*(-1)^k. - Juri-Stepan Gerasimov, Jul 30 2009

Programs

Maple

A129768 := proc(n) local res,p,i ; res := 0 ; p := ithprime(n) ; for i from 1 to p-1 by 2 do if not isprime(i) then res := res+1 ; fi ; od ; RETURN(res) ; end: for n from 1 to 80 do printf("%d, ",A129768(n)) ; od ; # R. J. Mathar, May 17 2007

Mathematica

f[n_] := Ceiling[ Prime@n / 2] - n + 1; Array[f, 72] (* Robert G. Wilson v *)
nn=401;With[{np=Select[Range[1,nn,2],!PrimeQ[#]&]},Table[Count[np,?(#<n&)],{n,Prime[Range[PrimePi[nn]]]}]] (* _Harvey P. Dale, Mar 01 2015 *)

Formula

a(n)=A008507(n-1)+1. - R. J. Mathar, Jul 06 2009

a(n)=sum_{k=A005843(n)..A006005(n)}-k*(-1)^k. - Juri-Stepan Gerasimov, Jul 30 2009

Extensions

Edited, corrected and extended by Robert G. Wilson v and R. J. Mathar, May 16 2007