A070184 Primes p such that x^8 = 2 has a solution mod p, but x^(8^2) = 2 has no solution mod p.
257, 1217, 1249, 1553, 1777, 2113, 2657, 2833, 4049, 4273, 4481, 4993, 5297, 6449, 6481, 6689, 7121, 7489, 8081, 8609, 9137, 9281, 9649, 10177, 10337, 10369, 10433, 11329, 11617, 11633, 12241, 12577, 13121, 13441, 13633, 14321, 14753, 15073, 15121, 15569, 16417, 16433, 16673, 17137
Offset: 1
Links
- M. F. Hasler, Table of n, a(n) for n = 1..2000, Jun 22 2024
Programs
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Magma
[p: p in PrimesUpTo(15000) | not exists{x: x in ResidueClassRing(p) | x^64 eq 2} and exists{x: x in ResidueClassRing(p) | x^8 eq 2}]; // Vincenzo Librandi, Sep 21 2012 -
PARI
ok(p, r, k1, k2)={ if ( Mod(r,p)^((p-1)/gcd(k1,p-1))!=1, return(0) ); if ( Mod(r,p)^((p-1)/gcd(k2,p-1))==1, return(0) ); return(1); } forprime(p=2,10^5, if (ok(p,2,8,8^2),print1(p,", "))); /* Joerg Arndt, Sep 21 2012 */ -
PARI
select( {is_A070184(p)=Mod(2,p)^(p\gcd(8,p-1))==1 && Mod(2,p)^(p\gcd(64,p-1))!=1 && isprime(p)}, primes(1999)) \\ The only composite numbers that would pass the test without isprime are A242880. - M. F. Hasler, Jun 22 2024 -
Python
from itertools import islice from sympy import is_nthpow_residue, nextprime def A070184_gen(startvalue=2): # generator of terms >= startvalue p = max(1,startvalue-1) while (p:=nextprime(p)): if is_nthpow_residue(2,8,p) and not is_nthpow_residue(2,64,p): yield p A070184_list = list(islice(A070184_gen(),10)) # Chai Wah Wu, Jun 23 2024
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