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A178128 Lesser of twin primes if it is a Ramanujan prime. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)