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

1,1

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]

Links

Table of n, a(n) for n=1..44.

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.

Formula

A164368 \ A104272.

Example

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]

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 *)

Crossrefs

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

Sequence in context: A253155 A095609 A046295 * A325074 A182476 A182451

Adjacent sequences: A164285 A164286 A164287 * A164289 A164290 A164291

Keyword

nonn

Author

Vladimir Shevelev, Aug 12 2009

Extensions

I added 521. - Vladimir Shevelev, Aug 17 2009

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

Status

approved