A225184 Primes p with a primitive root that divides p+1.
2, 3, 5, 11, 13, 17, 19, 29, 37, 41, 53, 59, 61, 67, 83, 89, 97, 101, 107, 109, 113, 131, 137, 139, 149, 163, 173, 179, 181, 197, 211, 227, 229, 233, 251, 257, 269, 281, 293, 307, 317, 347, 349, 353, 373, 379, 389, 401, 419, 421, 433, 443, 449, 461, 467, 491, 499, 509, 521, 523, 541, 547, 557, 563, 569, 587, 593, 601
Offset: 1
Keywords
Examples
The primitive roots modulo 97 are 5, 7, 10, 13, 14, 15, 17, 21, 23, 26, 29, 37, 38, 39, ..., and 7 divides 98, so 97 is a member of this sequence.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
- Arto Lepistö, Francesco Pappalardi and Kalle Saari, Transposition Invariant Words, Theoret. Comput. Sci., Vol. 380, No. 3 (2007), pp. 377-387.
Programs
-
Magma
[p: p in PrimesUpTo(700) | exists{r: r in [1..p-1] | IsPrimitive(r,p) and IsZero((p+1) mod r)}]; // Bruno Berselli, May 10 2013 -
PARI
forprime(p=2,1000, i=0; fordiv(p+1,X, if(znorder(Mod(X,p))==eulerphi(p), i=1)); if(i==1,print1(p", "))) \\ V. Raman, May 04 2013
Extensions
More terms from V. Raman, May 04 2013