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

%I A363215 #18 May 22 2023 14:18:23
%S A363215 2,11,13,23,47,59,71,83,107,109,121,131,167,179,181,191,227,229,239,
%T A363215 251,263,277,286,311,313,347,359,383,419,421,431,433,443,467,479,491,
%U A363215 503,541,563,587,599,601,647,659,683,709,719,733,743,757,827,829,839,863
%N A363215 Integers p > 1 such that 3^d == 1 (mod p) where d = A000265(p-1).
%C A363215 Inspired by an incorrect definition of strong pseudoprime to base 3.
%C A363215 As is obvious from the data, it fails to include all primes. Does include some composite numbers (pseudoprimes), namely 121, 286, 24046, 47197, 82513, ...
%H A363215 Jeppe Stig Nielsen, <a href="/A363215/b363215.txt">Table of n, a(n) for n = 1..10000</a>
%H A363215 Wikipedia, <a href="https://en.wikipedia.org/wiki/Strong_pseudoprime">Strong pseudoprime</a>
%o A363215 (PARI) is(p)=my(d=p-1);d/=2^valuation(d,2);Mod(3,p)^d==1
%o A363215 (Python)
%o A363215 from itertools import count, islice
%o A363215 def inA363215(n): return pow(3,n-1>>(~(n-1)&n-2).bit_length(),n)==1
%o A363215 def A363215_gen(startvalue=2): # generator of terms >= startvalue
%o A363215     return filter(inA363215,count(max(startvalue,2)))
%o A363215 A363215_list = list(islice(A363215_gen(),20)) # _Chai Wah Wu_, May 22 2023
%Y A363215 Cf. A000265, A005935, A020229, A130433.
%K A363215 nonn
%O A363215 1,1
%A A363215 _Jeppe Stig Nielsen_, May 21 2023