A363215 Integers p > 1 such that 3^d == 1 (mod p) where d = A000265(p-1).

2, 11, 13, 23, 47, 59, 71, 83, 107, 109, 121, 131, 167, 179, 181, 191, 227, 229, 239, 251, 263, 277, 286, 311, 313, 347, 359, 383, 419, 421, 431, 433, 443, 467, 479, 491, 503, 541, 563, 587, 599, 601, 647, 659, 683, 709, 719, 733, 743, 757, 827, 829, 839, 863

Offset: 1

Author

Jeppe Stig Nielsen, May 21 2023

Keywords

• nonn

Comments

Inspired by an incorrect definition of strong pseudoprime to base 3.

As is obvious from the data, it fails to include all primes. Does include some composite numbers (pseudoprimes), namely 121, 286, 24046, 47197, 82513, ...

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..10000
• Wikipedia, Strong pseudoprime

Crossrefs

Cf. A000265, A005935, A020229, A130433.

Programs

PARI

is(p)=my(d=p-1);d/=2^valuation(d,2);Mod(3,p)^d==1

Python

from itertools import count, islice
def inA363215(n): return pow(3,n-1>>(~(n-1)&n-2).bit_length(),n)==1
def A363215_gen(startvalue=2): # generator of terms >= startvalue
    return filter(inA363215,count(max(startvalue,2)))
A363215_list = list(islice(A363215_gen(),20)) # Chai Wah Wu, May 22 2023