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A062046 Sum of even numbers between consecutive primes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 1 00:27 EDT 2020. Contains 334756 sequences. (Running on oeis4.)