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A062047
Sum of odd numbers between consecutive primes.
1
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
1,4
LINKS
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
Sequence in context: A320379 A308102 A338016 * A117465 A136679 A299154
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