A164288 Members of A164368 which are not Ramanujan primes.

109, 137, 191, 197, 283, 521, 617, 683, 907, 991, 1033, 1117, 1319, 1493, 1619, 1627, 1697, 1741, 1747, 1801, 1931, 1949, 2011, 2111, 2143, 2153, 2293, 2417, 2539, 2543, 2549, 2591, 2621, 2837, 2927, 2953, 2969, 3079, 3119, 3187, 3203, 3329, 3389, 3407

Offset: 1

Author

Vladimir Shevelev, Aug 12 2009

Keywords

• nonn

Comments

Every lesser of twin primes (A001359), beginning with 137, which is not in A104272, is in the sequence. [From Vladimir Shevelev, Aug 31 2009]

Examples

			p=137 is the least lesser of twin primes which is not a Ramanujan prime. Therefore it is in the sequence. [From _Vladimir Shevelev_, Aug 31 2009]
		

Links

• J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, arXiv:1105.2249 [math.NT], 2011; J. Integer Seq. 14 (2011) Article 11.6.2.
• V. Shevelev, On critical small intervals containing primes, arXiv:0908.2319 [math.NT], 2009.
• V. Shevelev, Ramanujan and Labos Primes, Their Generalizations, and Classifications of Primes, J. Int. Seq. 15 (2012) # 12.5.4.

Crossrefs

Cf. A104272, A001262, A001567, A062568, A141232.

Programs

Mathematica

nn = 250;
A164368 = Select[Prime[Range[2 nn]], PrimePi[2 NextPrime[#/2]] != PrimePi[#]&];
Rama = Table[0, {nn}]; s = 0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, Rama[[s+1]] = k], {k, Prime[3 nn]}];
A104272 = Rama+1;
Complement[A164368, A104272] (* Jean-François Alcover, Oct 27 2018, after T. D. Noe in A104272 *)

Formula

A164368 \ A104272.

Extensions

I added 521. - Vladimir Shevelev, Aug 17 2009

Redefined in terms of A164368 and extended by R. J. Mathar, Aug 18 2009