A163639 The count of odd numbers from prime(n) up to the n-th odd nonprime, A014076(n).

1, 4, 6, 8, 8, 8, 9, 9, 9, 9, 10, 8, 8, 8, 9, 7, 6, 8, 6, 6, 7, 5, 5, 3, 2, 2, 2, 3, 4, 3, 5, 6, 8, 8, 11, 10, 12, 12, 13, 15, 17, 15, 19, 18, 19, 18, 22, 27, 27, 27, 26, 28, 28, 32, 32, 32, 34, 34, 36, 37, 36, 40, 46, 47, 47, 47, 51, 52, 56, 54, 55, 57, 60, 61, 63, 63, 65, 67, 68, 69

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 02 2009

Keywords

• nonn

Comments

The count includes these two odd numbers themselves and is conducted in both directions with a positive result independent of which of the two limits is larger.

Examples

			a(2)=4 counts the 4 numbers 3, 5, 7, and 9;
a(3)=6 counts the 6 numbers 5, 7, 9, 11, 13, and 15.
		

Crossrefs

Cf. A000040, A005408, A014076.

Programs

Maple

A014076 := proc(n) if n = 1 then 1; else for a from procname(n-1)+2 by 2 do if not isprime(a) then RETURN(a) ; fi; od: fi; end:
A163639 := proc(n) if n = 1 then 1; else onpr := A014076(n) ; pr := ithprime(n) ; 1+(max(onpr,pr)-min(onpr,pr))/2 fi; end:
seq(A163639(n),n=1..100) ; # R. J. Mathar, Aug 06 2009

Formula

a(n) = 1 + (M-m)/2, n > 1, where M = max(A000040(n), A014076(n)) and m = min(A000040(n), A014076(n)).

Extensions

Edited and corrected R. J. Mathar, Aug 06 2009