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

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, 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, 36, 36, 6, 8, 12, 36, 10, 0, 0, 24, 0, 22, 54, 30, 0, 14, 12, 18, 22

Offset: 1

Author

Vladimir Shevelev, Aug 18 2011

Keywords

• nonn

Comments

Conjecture: Asymptotic density of nonzero terms is 3/4.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes
• J. Sondow, Ramanujan Prime. (MathWorld)

Crossrefs

Cf. A104272, A080359, A193507, A194184, A194186.

Programs

Mathematica

nn = 100;
R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s+1]] = k], {k, Prime[3nn]}
];
A104272 = R = R + 1;
T = Table[0, {nn + 1}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s <= nn && T[[s+1]] == 0, T[[s+1]] = k], {k, Prime[3nn]}
];
A080359 = Rest[T];
A104272 - A080359 (* Jean-François Alcover, Aug 19 2018, after T. D. Noe *)