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.
%I A160273 #24 Jul 03 2021 21:39:23 %S A160273 1,1,2,2,3,2,5,1,5,2,5,2,1,5,2,5,2,5,6,12,2,5,10,8,5,3,4,3,25,2,1,5,4, %T A160273 23,2,3,2,5,10,13,8,2,2,3,18,4,5,1,20,2,8,5,4,11,14,1,9,3,8,5,9,1,4,3 %N A160273 Successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040). %C A160273 From _Eric Snyder_, Jul 02 2021: (Start) %C A160273 Also the successive differences of A002822. %C A160273 Instances of a(n) = 1 correspond to prime quadruples. (End) %H A160273 Eric Snyder, <a href="/A160273/b160273.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Harvey P. Dale) %p A160273 ZL := []; for p to 1000000 do if `and`(isprime(p), isprime(p+2)) then ZL := [op(ZL), ((p+2)^2-p^2)*(1/8)] end if end do; a := [seq((ZL[i+1]-ZL[i])*(1/3), i = 2 .. nops(ZL)-1)] %t A160273 Rest[(Differences[(Mean/@Select[Partition[Prime[Range[500]],2,1], #[[2]]- #[[1]]==2&])/2])/3] (* _Harvey P. Dale_, Jun 10 2014 *) %Y A160273 Cf. A040040, A002822. %K A160273 nonn %O A160273 1,3 %A A160273 _Stephen Crowley_, May 07 2009 %E A160273 Keyword "hard" deleted by _Harvey P. Dale_, Jun 10 2014