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