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

1,1

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.

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.

Formula

A001359 intersect A104272.

Example

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

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 *)

Prog

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

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).

Sequence in context: A128464 A105170 A162175 * A330410 A111255 A060213

Adjacent sequences: A178125 A178126 A178127 * A178129 A178130 A178131

Keyword

nonn

Author

Jonathan Sondow, May 20 2010

Status

approved