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

1,2

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.

Links

Table of n, a(n) for n=1..80.

Formula

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

Example

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.

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

Crossrefs

Cf. A000040, A005408, A014076.

Sequence in context: A352421 A159576 A199626 * A196355 A095253 A027709

Adjacent sequences: A163636 A163637 A163638 * A163640 A163641 A163642

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 02 2009

Extensions

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

Status

approved