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 A164288 Members of A164368 which are not Ramanujan primes. 27
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 8 12:20 EDT 2024. Contains 375021 sequences. (Running on oeis4.)