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%I #9 Feb 11 2024 13:18:09
%S 7,19,13,67,103,7,199,7,109,13,487,193,7,787,7,13,19,433,1447,7,19,7,
%T 13,769,2503,2707,7,43,7,1201,3847,4099,1453,7,4903,7,5479,5779,2029,
%U 19,7,13,7,61,37,8467,8839,7,13,7,3469,31,11239,3889,7,12547,7,43,19,4801
%N Smallest prime divisor of 4n^2+3 that is of the form 6k+1.
%C Any prime divisor of 4n^2+3 different from 3 is congruent to 1 modulo 6.
%C 4n^2+3 is never a power of 3 for n > 0; hence a prime divisor congruent to 1 modulo 6 always exists.
%C a(n) = 7 if and only if n is congruent to 1 or -1 modulo 7.
%D D. M. Burton, Elementary Number Theory, McGraw-Hill, Sixth Edition (2007), p. 191.
%H Nick Hobson, <a href="/A125257/b125257.txt">Table of n, a(n) for n = 1..1000</a>
%e The prime divisors of 4*3^2+3=39 are 3 and 13, so a(3) = 13.
%o (PARI) vector(60, n, factor(4*n^2+3)[2-(n^2)%3,1])
%Y Cf. A057204, A124988.
%K easy,nonn
%O 1,1
%A _Nick Hobson_, Nov 26 2006
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