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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
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.
FORMULA
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
Sequence in context: A253155 A095609 A046295 * A325074 A182476 A182451
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 March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)