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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A104272, A001359, A164288, A164554

Sequence in context: A180541 A103993 A088269 * A225672 A355803 A240125

Adjacent sequences: A164368 A164369 A164370 * A164372 A164373 A164374

Keyword

nonn

Author

Vladimir Shevelev, Aug 14 2009, Aug 17 2009

Extensions

Extended by R. J. Mathar, Sep 17 2009

Status

approved