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

1,2

Comments

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

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A113610 A309334 A263319 * A102020 A125133 A109310

Adjacent sequences: A062043 A062044 A062045 * A062047 A062048 A062049

Keyword

nonn

Author

Amarnath Murthy, Jun 06 2001

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

Status

approved