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A156902
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Primes p such that there is no multiple of (the order of p among the primes) between p and q, where q is the smallest prime > p.
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11, 13, 17, 19, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 101, 103, 107, 109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If pi(p) is the order of the prime p, then p is included in the sequence if pi(p)*ceiling(p/pi(p)) > the (pi(p)+1)th prime.
The sequence of primes not in the list is less dense: 2, 3, 5, 7, 23, 29, 31, 89, 97, 113, 317, 331, 337, 349, 353, 359, 997, 1069, 1091, 1109, 1117, 1123, 1129, 3049, 3061, 3067, 3079, 3083, 3089... [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009]
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EXAMPLE
| 37 is the 12th prime. 41 is the 13th prime. Since there is no multiple of 12 between 37 and 41, then 37 is included in the sequence.
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MAPLE
| for n from 1 to 300 do p := ithprime(n) ; q := nextprime(p) ; if n*floor(q/n) < p then printf("%d, ", p) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009]
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CROSSREFS
| A068902
Sequence in context: A032590 A181576 A076162 * A050674 A164329 A159236
Adjacent sequences: A156899 A156900 A156901 * A156903 A156904 A156905
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Feb 17 2009
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EXTENSIONS
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 21 2009
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