A062047 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

LINKS

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

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.

EXAMPLE

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A001223, A062046.

Sequence in context: A320379 A308102 A338016 * A117465 A136679 A299154

Adjacent sequences: A062044 A062045 A062046 * A062048 A062049 A062050

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 06 2001

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

STATUS

approved