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

1,1

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

Prog

(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

Crossrefs

Cf. A000265, A005935, A020229, A130433.

Sequence in context: A045385 A090416 A090430 * A022115 A042453 A041885

Adjacent sequences: A363212 A363213 A363214 * A363216 A363217 A363218

Keyword

nonn

Author

Jeppe Stig Nielsen, May 21 2023

Status

approved