A242755 Primes p such that pi(p)*q == 1 (mod p) for some prime q < p, where pi(p) is the number of primes not exceeding p.

3, 5, 7, 13, 17, 29, 31, 41, 59, 61, 73, 127, 157, 173, 179, 199, 223, 227, 239, 241, 271, 281, 311, 317, 349, 353, 359, 367, 379, 419, 439, 479, 487, 503, 541, 557, 599, 643, 653, 709, 769, 773, 809, 823, 829, 839, 859, 941, 953, 1063

Offset

1,1

Comments

According to the conjecture in A242753, this sequence should contain infinitely many primes.

Conjecture: The number of such primes not exceeding x > 1 has the main term x/(log x)^2 as x tends to infinity.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(4) = 13 since 13 is prime with pi(13) = 6, and 6*11 == 1 (mod 13) with 11 prime, but pi(11)*9 == 1 (mod 11) with 9 not prime.

Mathematica

p[n_]:=PrimeQ[PowerMod[n, -1, Prime[n]]]
n=0; Do[If[p[k], n=n+1; Print[n, " ", Prime[k]]]; Continue, {k, 1, 179}]

Crossrefs

Cf. A000040, A000720, A242748, A242750, A242752, A242753, A242754.

Sequence in context: A177070 A247018 A038929 * A070806 A339506 A178490

Adjacent sequences: A242752 A242753 A242754 * A242756 A242757 A242758

Keyword

nonn

Author

Zhi-Wei Sun, May 22 2014

Status

approved