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 A259922 #26 Jul 19 2015 08:56:48
%S A259922 0,-1,-1,-2,2,1,1,1,-3,-4,-2,-3,1,1,-1,-2,6,6,6,6,3,2,4,3,3,3,1,1,5,4,
%T A259922 4,4,4,3,3,2,3,3,3,2,8,7,9,9,6,6,8,8,3,3,1,0,4,3,1,1,-3,-3,-1,-1,3,3,
%U A259922 3,2,2,1,3,3,0,-1,1,1,7,7,5,4,4,4,4,4,4,3
%N A259922 a(n)= Sum_{2 < prime p <= n} c_p - Sum_{n < prime p < 2*n} c_p, where 2^c_p is the greatest power of 2 dividing p-1.
%C A259922 It is known that, for n>10, pi(2*n) < 2*pi(n), where pi(n) is the number of primes not exceeding n (A000720). Thus, for n>10, in the interval (1,n] we have more primes than in the interval (n,2*n).
%C A259922 In connection with this, it is natural to conjecture that there exists a number N such that a(n)>0 for all n >= N.
%H A259922 Peter J. C. Moses, <a href="/A259922/b259922.txt">Table of n, a(n) for n = 1..2000</a>
%t A259922 Map[Total[Flatten[Map[IntegerExponent[Select[#,PrimeQ]-1,2]&,{Range[3,#],Range[#+1,2#-1]}]{1,-1}]]&,Range[50]]
%Y A259922 Cf. A007814, A060208, A259788, A259897.
%K A259922 sign
%O A259922 1,4
%A A259922 _Vladimir Shevelev_, Jul 09 2015
%E A259922 More terms from _Peter J. C. Moses_, Jul 09 2015