A178128 Lesser of twin primes if it is a Ramanujan prime.

11, 17, 29, 41, 59, 71, 101, 107, 149, 179, 227, 239, 269, 281, 311, 347, 419, 431, 461, 569, 599, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1427, 1451, 1481, 1487, 1607, 1667, 1721, 1787, 1871, 1877, 1997

Offset: 1

Author

Jonathan Sondow, May 20 2010

Keywords

• nonn

Comments

By definition, a number p is a member if p and p+2 are primes and p is a Ramanujan prime A104272.

Supersequence of A178127.

In the first 328 pairs of twin primes, more than 78% of their first members are Ramanujan primes. For a partial explanation, see "Ramanujan primes and Bertrand's postulate" Section 7.

See A001359 and A104272 for additional comments, links, and references.

Examples

			a(1) = 11 because 11 and 13 are the 1st twin primes the lesser of which is a Ramanujan prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009, 2010.
• J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly, 116 (2009), 630-635.
• 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. A001359 (lesser of twin primes), A104272 (Ramanujan primes), A164371 (lesser of twin prime pairs which are non-Ramanujan primes), A178127 (lesser of twin Ramanujan primes).

Programs

Mathematica

nn = 200; 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;
A001359 = Select[Prime[Range[2 nn]], PrimeQ[# + 2]&];
Intersection[A001359, A104272] (* Jean-François Alcover, Nov 07 2018, using T. D. Noe's code for A104262 *)

Perl

use ntheory ":all"; my @t = grep { is_prime($+2) } @{ramanujan_primes(10000)}; say "@t"; # _Dana Jacobsen, Sep 06 2015

Formula

A001359 intersect A104272.