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A164288
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Members of A164368 which are not Ramanujan primes.
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27
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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
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OFFSET
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1,1
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COMMENTS
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Every lesser of twin primes (A001359), beginning with 137, which is not in A104272, is in the sequence. [From Vladimir Shevelev, Aug 31 2009]
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LINKS
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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.
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FORMULA
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A164368 \ A104272.
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EXAMPLE
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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]
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A104272, A001262, A001567, A062568, A141232.
Sequence in context: A253155 A095609 A046295 * A325074 A182476 A182451
Adjacent sequences: A164285 A164286 A164287 * A164289 A164290 A164291
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev, Aug 12 2009
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EXTENSIONS
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I added 521. - Vladimir Shevelev, Aug 17 2009
Redefined in terms of A164368 and extended by R. J. Mathar, Aug 18 2009
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STATUS
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approved
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