%I #14 Jul 16 2022 17:15:36

%S 0,0,0,9,0,15,0,21,52,0,68,39,0,45,100,112,0,128,69,0,152,81,172,279,

%T 99,0,105,0,111,720,129,268,0,576,0,308,320,165,340,352,0,744,0,195,0,

%U 1025,1085,225,0,231,472,0,984,508,520,532,0,548,279,0,1152,1800,309,0

%N Sum of odd numbers between consecutive primes.

%H Harry J. Smith, <a href="/A062047/b062047.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = {prime(n+1) + prime(n)}*{prime(n+1) - prime(n)-2}/4.

%F a(n) = (prime(n)+e(n) )*( e(n)-1 ), where e(n) = A001223(n) / 2, for n > 1.

%e a(4) = 9 is the single odd number between 7 and 11.

%t Plus@@Range[ #[[1]]+2,#[[2]]-2,2]&/@Partition[Prime[Range[100]],2,1] (* _Harvey P. Dale_, Aug 13 2009 *)

%o (PARI) { for (n=1, 1000, q=prime(n + 1); p=prime(n); a=(q + p)*(q - p - 2)/4; if (n==1, a=0); write("b062047.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 30 2009

%Y Cf. A001223, A062046.

%K nonn

%O 1,4

%A _Amarnath Murthy_, Jun 06 2001

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, Jun 07 2001

%E OFFSET changed from 0 to 1 by _Harry J. Smith_, Jul 30 2009