A164371 The smaller members of twin prime pairs which are non-Ramanujan primes.

3, 5, 137, 191, 197, 521, 617, 1319, 1619, 1697, 1931, 1949, 2111, 2549, 2591, 2969, 3119, 3329, 3389, 3557, 3929, 4157, 4217, 4271, 4517, 5279, 5417, 7331, 7349, 7757, 8009, 8429, 8837, 9011, 9281, 9437, 9857, 9929, 10007, 10037, 10457, 10529, 10859

Offset: 1

Author

Vladimir Shevelev, Aug 14 2009, Aug 17 2009

Keywords

• nonn

Comments

The terms greater than 5 of the sequence are in A164288.

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..10000
• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2

Crossrefs

Cf. A104272, A001359, A164288, A164554

Programs

Mathematica

nn = 1000;
A001359 = Select[Prime[Range[2 nn]], PrimeQ[# + 2] &];
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[3 nn]}];
A104272 = R + 1;
Complement[A001359, A104272] (* Jean-François Alcover, Oct 28 2018, after T. D. Noe in A104272 *)

Perl

use ntheory ":all"; for (@{twin_primes(1e4)}) { say if !is_ramanujan_prime($) } # _Dana Jacobsen, Dec 30 2015

Formula

A001359 \ A104272. - R. J. Mathar, Sep 17 2009

Extensions

Extended by R. J. Mathar, Sep 17 2009