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Search: id:A164368
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| A164368 |
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Primes a(n) with the property: let q be the smallest prime > a(n)/2, then a prime exists between a(n) and 2q. |
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19
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| 2, 11, 17, 29, 41, 47, 59, 67, 71, 97, 101, 107, 109, 127, 137, 149, 151, 167, 179, 181, 191, 197, 227, 229, 233, 239, 241, 263, 269, 281, 283, 307, 311, 347, 349, 367, 373, 401, 409, 419, 431, 433, 439, 461, 487, 491, 503, 521, 569, 571
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The Ramanujan primes possess the following property:
If prime(n)>2 is a Ramanujan prime, then all integers (prime(n)+1)/2, (prime(n)+3)/2, ... , (prime(n+1)-1)/2 are composite numbers.
The sequence contains all primes with this property, whether Ramanujan or not.
All Ramanujan primes A104272 are in the sequence.
Every lesser of twin primes (A001359), beginning with 11, is in the sequence. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 31 2009]
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LINKS
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V. Shevelev, On critical small intervals containing primes [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 20 2009]
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EXAMPLE
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2 is in the sequence, since then q=2, and there is a prime 3 between 2 and 4. - N. J. A. Sloane, Oct 15 2009
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CROSSREFS
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Cf. A164332, A164333, A104272, A164288, A080359, A164294, A001262, A001567, A062568, A141232.
Sequence in context: A153222 A087379 A019364 this_sequence A104272 A117155 A141176
Adjacent sequences: A164365 A164366 A164367 this_sequence A164369 A164370 A164371
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Aug 14 2009
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