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 A226502 #16 Jul 14 2025 16:45:27 %S A226502 11,34,36,96,60,144,160,162,360,198,320,336,352,494,460,720,378,560, %T A226502 718,450,972,1020,938,1002,816,420,864,1752,960,2596,810,2204,576, %U A226502 2404,1220,1606,1980,1694,1420,2876,744,2694,780,3160,2810,3520,3170,1824,1840,1422,3836 %N A226502 Let P(k) denote the k-th prime (P(1)=2, P(2)=3 ...); a(n) = P(n+1)P(n+3) - P(n)P(n+2). %C A226502 Differences of the products of alternate primes. %H A226502 Harvey P. Dale, <a href="/A226502/b226502.txt">Table of n, a(n) for n = 1..1000</a> %F A226502 a(n) >> n log n and this is probably sharp: on Dickson's conjecture there are infinitely many a(n) < kn log n for any k > 4. The constant 4 comes from 8 + 2 - 6 - 0 n the prime quadruplet (p+0, p+2, p+6, p+8). On Cramér's conjecture a(n) = O(n log^3 n). Unconditionally a(n) << n^1.525 log n. - _Charles R Greathouse IV_, Jun 10 2013 %t A226502 #[[2]]#[[4]]-#[[1]]#[[3]]&/@Partition[Prime[Range[60]],4,1] (* _Harvey P. Dale_, Jul 14 2025 *) %o A226502 (PARI) p=2;q=3;r=5;forprime(s=7,1e2,print1(q*s-p*r", ");p=q;q=r;r=s) \\ _Charles R Greathouse IV_, Jun 10 2013 %Y A226502 First differences of A090076. %K A226502 nonn,easy %O A226502 1,1 %A A226502 _Ed Smiley_, Jun 09 2013