A173081 Number of twin prime pairs < 10^n that contain at least one Ramanujan prime (A104272).

0, 6, 28, 167, 964, 6305, 45082, 335919, 2605867, 20841010, 170395131

Offset: 1

Author

T. D. Noe, Nov 22 2010

Keywords

• nonn
• more

Comments

It appears that this gives the number of Ramanujan primes < 10^n that are the lesser prime in a twin prime pair. Equivalently, this sequence also gives the number of Ramanujan primes p with p+2 also prime less than 10^n.

It appears that no upper twin prime is a Ramanujan prime without the corresponding lower twin prime also being a Ramanujan prime.

This is proved in Section 4 of "Ramanujan Primes: Bounds, Runs, Twins, and Gaps".

Links

• 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. A178128 (Ramanujan primes p such that p+2 is prime), A007508 (number of twin primes pairs < 10^n), A181678 (number of twin Ramanujan primes pairs < 10^n).

Programs

Mathematica

nn=50000; t=Table[0,{nn}]; s=0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s
				

Extensions

a(10)-a(11) from Dana Jacobsen, Apr 29 2015