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

1,1

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

Links

Table of n, a(n) for n=1..55.

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

Adjacent sequences: A156899 A156900 A156901 * A156903 A156904 A156905

Keyword

nonn

Author

Leroy Quet, Feb 17 2009

Extensions

Extended by R. J. Mathar, Feb 21 2009

Status

approved