A062046 Sum of even numbers between consecutive primes.

0, 4, 6, 18, 12, 30, 18, 42, 78, 30, 102, 78, 42, 90, 150, 168, 60, 192, 138, 72, 228, 162, 258, 372, 198, 102, 210, 108, 222, 840, 258, 402, 138, 720, 150, 462, 480, 330, 510, 528, 180, 930, 192, 390, 198, 1230, 1302, 450, 228, 462, 708, 240, 1230, 762, 780

Offset: 1

Author

Amarnath Murthy, Jun 06 2001

Keywords

• nonn

Comments

First differences of A024701. - Gionata Neri, May 25 2015

Examples

			a(4) = 18 = 8+10 as the even numbers between 7 and 11 are 8 and 10. a(4) = (11+7)(11-7)/4 = 18.
		

Links

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

Crossrefs

a(n)= ( p(n) + e(n)) * e(n), e(n) := A001223(n) / 2, for n > 1

Programs

Mathematica

Total[Select[Range[#[[1]]+1,#[[2]]-1],EvenQ]]&/@ Partition[ Prime[ Range[ 60]],2,1] (* Harvey P. Dale, May 28 2013 *)

PARI

{ for (n=1, 1000, a=(prime(n + 1)^2 - prime(n)^2)/4; if (n==1, a=0); write("b062046.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 30 2009

Formula

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

Extensions

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

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