A360827 Primes p, not safe primes, such that the smallest factor of (2^(p-1)-1) / 3 is equal to p.

443, 647, 1847, 2243, 2687, 2699, 6263, 6563, 7487, 7583, 8627, 8663, 9419, 9767, 10223, 11867, 12323, 13187, 13907, 14627, 14723, 14783, 17747, 17783, 19739, 20639, 20807, 21863, 22307, 23747, 24107, 24923, 25127, 26759, 27983, 29207, 29819, 30839, 31247, 32303, 34403, 34439

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

443 is the first term since p = 443 is the first term of A359387 that is not in A005385 (i.e., (443-1)/2 = 13*17 is not prime).
647 is the second term since p = 647 is the first term (> 443) of A359387 that is not in A005385 (i.e., (647-1)/2 = 17*19 is not prime).

Mathematica

q[p_] := ! PrimeQ[(p - 1)/2] && AllTrue[Range[p], ! PrimeQ[#] || PowerMod[2, p - 1, 3*p*#] > 1 &]; Select[Prime[Range[4, 4000]], q] (* Amiram Eldar, Mar 01 2023 *)

Prog

(PARI) forprime(p=11, 40000, if(!isprime((p-1)/2), forprime(div=5, p-1, if(Mod(2, div)^(p-1)==1, next(2))); print1(p, ", ")))

Crossrefs

Equals A359387 \ A005385.

Sequence in context: A171392 A105980 A031519 * A031699 A158321 A293978

Adjacent sequences: A360824 A360825 A360826 * A360828 A360829 A360830

Keyword

nonn

Author

Alain Rocchelli, Feb 22 2023

Status

approved