A062047 Sum of odd numbers between consecutive primes.

0, 0, 0, 9, 0, 15, 0, 21, 52, 0, 68, 39, 0, 45, 100, 112, 0, 128, 69, 0, 152, 81, 172, 279, 99, 0, 105, 0, 111, 720, 129, 268, 0, 576, 0, 308, 320, 165, 340, 352, 0, 744, 0, 195, 0, 1025, 1085, 225, 0, 231, 472, 0, 984, 508, 520, 532, 0, 548, 279, 0, 1152, 1800, 309, 0

Offset: 1

Author

Amarnath Murthy, Jun 06 2001

Keywords

• nonn

Examples

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

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A001223, A062046.

Programs

Mathematica

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

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

Formula

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

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

Extensions

More terms from Larry Reeves (larryr(AT)acm.org) and Jason Earls, Jun 07 2001

OFFSET changed from 0 to 1 by Harry J. Smith, Jul 30 2009