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A194217 a(n) = A104272(n)-A080359(n).

%I A194217 #20 Feb 16 2025 08:33:15
%S A194217 0,8,4,10,10,4,6,6,0,24,0,4,18,36,12,10,6,0,36,36,34,0,0,12,0,10,24,
%T A194217 18,34,0,14,0,22,0,0,10,0,0,18,24,0,4,60,48,10,0,0,0,0,28,24,0,0,0,16,
%U A194217 36,36,6,8,12,36,10,0,0,24,0,22,54,30,0,14,12,18,22
%N A194217 a(n) = A104272(n)-A080359(n).
%C A194217 Conjecture: Asymptotic density of nonzero terms is 3/4.
%H A194217 Alois P. Heinz, <a href="/A194217/b194217.txt">Table of n, a(n) for n = 1..1000</a>
%H A194217 V. Shevelev, <a href="http://arxiv.org/abs/0909.0715">Ramanujan and Labos primes, their generalizations and classifications of primes</a>
%H A194217 J. Sondow, <a href="https://mathworld.wolfram.com/RamanujanPrime.html">Ramanujan Prime</a>. (MathWorld)
%t A194217 nn = 100;
%t A194217 R = Table[0, {nn}]; s = 0;
%t A194217 Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s+1]] = k], {k, Prime[3nn]}
%t A194217 ];
%t A194217 A104272 = R = R + 1;
%t A194217 T = Table[0, {nn + 1}]; s = 0;
%t A194217 Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s <= nn && T[[s+1]] == 0, T[[s+1]] = k], {k, Prime[3nn]}
%t A194217 ];
%t A194217 A080359 = Rest[T];
%t A194217 A104272 - A080359 (* _Jean-François Alcover_, Aug 19 2018, after _T. D. Noe_ *)
%Y A194217 Cf. A104272, A080359, A193507, A194184, A194186.
%K A194217 nonn
%O A194217 1,2
%A A194217 _Vladimir Shevelev_, Aug 18 2011