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 A248891 #8 Nov 28 2014 21:55:08 %S A248891 1,1,1,1,1,2,2,2,3,2,4,3,4,4,3,4,3,3,2,1,2,3,2,2,5,4,3,2,1,1,4,3,2,3, %T A248891 4,6,5,4,3,4,5,6,7,6,5,4,5,5,5,4,5,4,5,5,5,6,9,8,8,7,7,7,8,7,6,6,5,4, %U A248891 3,3,3,2,7,6,5,5,5,4,3,2,5,5,8,9,11,10,10,9,9,8,7,7,6,6,6,5,4,5,8,8 %N A248891 Number of primes p such that p+2 is prime and A001359(n) < p < A001359(n)^(1+1/n). %C A248891 Conjecture: For every positive integer n, A001359(n+1)^(1/(n+1)) < A001359(n)^(1/n). Note that this conjecture is equivalent to " A001359 is infinite and for every n, A001359(n+1) < A001359(n)^(1+1/n). This implies for every n, a(n) is positive. See comment lines of the sequence A001359. %e A248891 Take n=1, A001359(1)=3, 3 < 5 < 3^(1+1/1)=9 hence a(1)=1. %e A248891 Take n=6, A001359(6)=41, 41 < 59 < 71 < 41^(1+1/6)~76.13 hence a(6)=2. %Y A248891 Cf. A001359, A248901, A248902, A248903. %K A248891 nonn %O A248891 1,6 %A A248891 _Jahangeer Kholdi_ and _Farideh Firoozbakht_, Nov 22 2014