A062046 - OEIS

%I #19 Jan 26 2019 11:32:38

%S 0,4,6,18,12,30,18,42,78,30,102,78,42,90,150,168,60,192,138,72,228,

%T 162,258,372,198,102,210,108,222,840,258,402,138,720,150,462,480,330,

%U 510,528,180,930,192,390,198,1230,1302,450,228,462,708,240,1230,762,780

%N Sum of even numbers between consecutive primes.

%C First differences of A024701. - _Gionata Neri_, May 25 2015

%H Harry J. Smith, <a href="/A062046/b062046.txt">Table of n, a(n) for n=1..1000</a>

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

%e 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.

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

%o (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

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

%K nonn

%O 1,2

%A _Amarnath Murthy_, Jun 06 2001

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

%E Offset changed from 0 to 1 by _Harry J. Smith_, Jul 30 2009