cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A062046 Sum of even numbers between consecutive primes.

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%I A062046 #19 Jan 26 2019 11:32:38
%S A062046 0,4,6,18,12,30,18,42,78,30,102,78,42,90,150,168,60,192,138,72,228,
%T A062046 162,258,372,198,102,210,108,222,840,258,402,138,720,150,462,480,330,
%U A062046 510,528,180,930,192,390,198,1230,1302,450,228,462,708,240,1230,762,780
%N A062046 Sum of even numbers between consecutive primes.
%C A062046 First differences of A024701. - _Gionata Neri_, May 25 2015
%H A062046 Harry J. Smith, <a href="/A062046/b062046.txt">Table of n, a(n) for n=1..1000</a>
%F A062046 a(n) = (prime(n+1)+prime(n))*(prime(n+1)-prime(n))/4 = (prime(n+1)^2-prime(n)^2)/4.
%e A062046 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 A062046 Total[Select[Range[#[[1]]+1,#[[2]]-1],EvenQ]]&/@ Partition[ Prime[ Range[ 60]],2,1] (* _Harvey P. Dale_, May 28 2013 *)
%o A062046 (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 A062046 a(n)= ( p(n) + e(n)) * e(n), e(n) := A001223(n) / 2, for n > 1
%K A062046 nonn
%O A062046 1,2
%A A062046 _Amarnath Murthy_, Jun 06 2001
%E A062046 More terms from Larry Reeves (larryr(AT)acm.org), Jun 07 2001
%E A062046 Offset changed from 0 to 1 by _Harry J. Smith_, Jul 30 2009