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A060914 Integers i > 1 for which there are two primes p such that i is a solution mod p of x^3 = 2. 5

%I

%S 7,16,20,21,26,32,34,45,49,50,52,54,57,58,61,70,72,79,81,86,92,94,98,

%T 103,111,112,114,116,119,122,125,130,136,137,141,143,147,152,157,160,

%U 170,176,179,181,184,186,197,198,199,214,221,222,225,231,234,236,240

%N Integers i > 1 for which there are two primes p such that i is a solution mod p of x^3 = 2.

%C Solutions mod p are represented by integers from 0 to p - 1. The following equivalences holds for i > 1: There is a prime p such that i is a solution mod p of x^3 = 2 iff i^3 - 2 has a prime factor > i; i is a solution mod p of x^3 = 2 iff p is a prime factor of i^3 - 2 and p > i. i^3 - 2 has at most two prime factors > i. For i such that i^3 - 2 has no prime factors > i; cf. A060591.

%F a(n) = n-th integer i such that i^3 - 2 has two prime factors > i.

%e a(3) = 20, since 20 is (after 7 and 16) the third integer i for which there are two primes p > i (viz. 31 and 43) such that i is a solution mod p of x^3 = 2, or equivalently, 20^3 - 2 = 7998 = 2*3*31*43 has two prime factors > 20. (cf. A059940).

%Y A040028, A059940, A060591.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 08 2001

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Last modified October 18 08:18 EDT 2021. Contains 348066 sequences. (Running on oeis4.)