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A225888 Primes p such that neither 2 nor 3 are primitive roots, but together 2 and 3 generate the nonzero residues mod p. 1
41, 103, 109, 151, 157, 229, 251, 271, 277, 367, 397, 683, 733, 761, 967, 971, 991, 1051, 1069, 1163, 1181, 1289, 1303, 1429, 1471, 1543, 1759, 1783, 1789, 1811, 1879, 2003, 2297, 2411, 2441, 2551, 2749, 2791, 2887, 2917, 3061, 3079, 3109, 3229, 3251, 3301, 3319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

2 has multiplicative order 20 mod 41, 3 has order 8 mod 41 so neither is a primitive root. The subgroup 2 and 3 generate together will have order lcm(20,8) = 40 so 2 and 3 generate all nonzero residues.

PROG

(PARI) is(n)=if(n>40 && isprime(n), my(a=znorder(Mod(2, n)), b); if(a==n-1, return(0)); b=znorder(Mod(3, n)); b<n-1 && lcm(a, b)==n-1, 0) \\ Charles R Greathouse IV, May 19 2013

CROSSREFS

Cf. A001122, A001123.

Sequence in context: A309934 A126588 A142794 * A156971 A123043 A142014

Adjacent sequences:  A225885 A225886 A225887 * A225889 A225890 A225891

KEYWORD

nonn

AUTHOR

John L. Drost, May 19 2013

STATUS

approved

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Last modified September 16 07:19 EDT 2021. Contains 347469 sequences. (Running on oeis4.)