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.

A062047 Sum of odd numbers between consecutive primes.

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%I A062047 #14 Jul 16 2022 17:15:36
%S A062047 0,0,0,9,0,15,0,21,52,0,68,39,0,45,100,112,0,128,69,0,152,81,172,279,
%T A062047 99,0,105,0,111,720,129,268,0,576,0,308,320,165,340,352,0,744,0,195,0,
%U A062047 1025,1085,225,0,231,472,0,984,508,520,532,0,548,279,0,1152,1800,309,0
%N A062047 Sum of odd numbers between consecutive primes.
%H A062047 Harry J. Smith, <a href="/A062047/b062047.txt">Table of n, a(n) for n=1..1000</a>
%F A062047 a(n) = {prime(n+1) + prime(n)}*{prime(n+1) - prime(n)-2}/4.
%F A062047 a(n) = (prime(n)+e(n) )*( e(n)-1 ), where e(n) = A001223(n) / 2, for n > 1.
%e A062047 a(4) = 9 is the single odd number between 7 and 11.
%t A062047 Plus@@Range[ #[[1]]+2,#[[2]]-2,2]&/@Partition[Prime[Range[100]],2,1] (* _Harvey P. Dale_, Aug 13 2009 *)
%o A062047 (PARI) { for (n=1, 1000, q=prime(n + 1); p=prime(n); a=(q + p)*(q - p - 2)/4; if (n==1, a=0); write("b062047.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 30 2009
%Y A062047 Cf. A001223, A062046.
%K A062047 nonn
%O A062047 1,4
%A A062047 _Amarnath Murthy_, Jun 06 2001
%E A062047 More terms from Larry Reeves (larryr(AT)acm.org) and _Jason Earls_, Jun 07 2001
%E A062047 OFFSET changed from 0 to 1 by _Harry J. Smith_, Jul 30 2009