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.

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

Author

Leroy Quet, Feb 17 2009

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

Cf. A068902.

Programs

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

Extensions

Extended by R. J. Mathar, Feb 21 2009