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 A218245 #20 Dec 07 2015 22:40:32
%S A218245 2,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A218245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A218245 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A218245 Nicolas's sequence, whose nonnegativity is equivalent to the Riemann hypothesis.
%C A218245 a(n) = floor(p(n)#/phi(p(n)#) - log(log(p(n)#))*exp(gamma)), where p(n)# is the n-th primorial, phi is Euler's totient function, and gamma is Euler's constant.
%C A218245 J.-L. Nicolas proved that all terms are >= 0 if and only if the Riemann hypothesis (RH) is true. In fact, results in his 2012 paper imply that RH is equivalent to a(n) = 0 for n > 6. Nicolas's refinement of this result is in A233825.
%C A218245 He also proved that if RH is false, then infinitely many terms are >= 0 and infinitely many terms are < 0.
%C A218245 See Nicolas's sequence A216868 for references, links, and additional cross-refs.
%F A218245 a(n) = [p(n)#/phi(p(n)#) - log(log(p(n)#))*exp(gamma)].
%F A218245 a(n) = [A002110(n)/A005867(n) - log(log(A002110(n)))*e^gamma].
%e A218245 p(2)# = 2*3 = 6 and phi(6) = 2, so a(2) = [6/2 - log(log(6))*e^gamma] = [3-0.58319...*1.78107...] = [3-1.038...] = 1.
%t A218245 primorial[n_] := Product[Prime[k], {k, n}]; Table[ With[{p = primorial[n]}, Floor[N[p/EulerPhi[p] - Log[Log[p]]*Exp[EulerGamma]]]], {n, 1, 100}]
%Y A218245 Cf. A216868, A233825.
%K A218245 nonn
%O A218245 1,1
%A A218245 _Jonathan Sondow_, Oct 24 2012