A308510 Prime(k) such that the multiplicative order of prime(k) (mod prime(k+1)) = prime(k+1)-1.

2, 3, 5, 7, 11, 19, 43, 59, 61, 67, 79, 83, 101, 103, 127, 131, 139, 151, 163, 179, 181, 197, 223, 251, 257, 269, 271, 307, 317, 337, 347, 353, 367, 379, 419, 421, 439, 443, 461, 463, 467, 487, 499, 523, 541, 563, 577, 587, 593, 607, 643, 659, 691, 709, 727, 733, 739

Offset: 1

Author

David James Sycamore, Jun 02 2019

Keywords

• nonn

Comments

Prime(k) is a term iff it is a primitive root of prime(k+1). These primes correspond to the records of A226295; if A226295(k) is such a record then prime(k) is a term in this sequence.

Examples

			A226295(14) = 46 is a record, so prime(14)=43 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A226295.

Programs

Mathematica

Select[Range[740], PrimeQ[#] && MultiplicativeOrder[#, p=NextPrime[#]] == p-1 &] (* Amiram Eldar, Jul 04 2019 *)

PARI

isok(p) = isprime(p) && (q=nextprime(p+1)) && (znorder(Mod(p, q)) == q-1) \\ Michel Marcus, Jun 02 2019

Extensions

More terms from Michel Marcus, Jun 02 2019