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A163639
The count of odd numbers from prime(n) up to the n-th odd nonprime, A014076(n).
1
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.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited and corrected R. J. Mathar, Aug 06 2009
STATUS
approved