Search: id:A059772
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%I A059772
%S A059772 0,7,7,23,17,47,31,79,0,17,71,167,97,223,127,41,23,359,199,439,241,31,
%T A059772 41,89,337,727,0,839,449,137,73,1087,577,1223,647,1367,103,0,47,73,881,
%U A059772 1847,967,0,151,2207,1151,2399,1249,113,193,401,0,3023,1567,191,0,71
%N A059772 Smallest prime p such that n is a solution mod p of x^2 = 2, or 0 if 
               no such prime exists.
%C A059772 Solutions mod p are represented by integers from 0 to p-1. The following 
               equivalences holds for n > 1: There is a prime p such that n is a 
               solution mod p of x^2 = 2 iff n^2-2 has a prime factor > n; n is 
               a solution mod p of x^2 = 2 iff p is a prime factor of n^2-2 and 
               p > n. n^2-2 has at most one prime factor > n, consequently such 
               a factor is the only prime p such that n is a solution mod p of x^2 
               = 2. For n such that n^2-2 has no prime factor > n (the zeros in 
               the sequence), cf. A060515.
%F A059772 If n^2-2 has a (unique) prime factor p > n, then a(n) = p, else a(n) 
               = 0.
%e A059772 a(11) = 17, since 11 is a solution mod 17 of x^2 = 2 and 11 is not a 
               solution mod p of x^2 = 2 for primes p < 17. Although 11^2 = 2 mod 
               7, prime 7 is excluded because 7 < 11 and 11 = 4 mod 7.
%Y A059772 Cf. A038873, A059770, A059771, A060515.
%Y A059772 Sequence in context: A146466 A146141 A062368 this_sequence A114369 A027844 
               A111217
%Y A059772 Adjacent sequences: A059769 A059770 A059771 this_sequence A059773 A059774 
               A059775
%K A059772 nonn
%O A059772 2,2
%A A059772 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 21 2001
%E A059772 Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 
               21 2009

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