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A156902
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.
0
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
OFFSET
1,1
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, ... - R. J. Mathar, Feb 21 2009
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.
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: # R. J. Mathar, Feb 21 2009
CROSSREFS
Cf. A068902.
Sequence in context: A032590 A181576 A076162 * A050674 A164329 A159236
KEYWORD
nonn
AUTHOR
Leroy Quet, Feb 17 2009
EXTENSIONS
Extended by R. J. Mathar, Feb 21 2009
STATUS
approved