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A379352 a(n) is the smallest nonnegative integer k such the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

%I A379352 #11 Dec 22 2024 23:56:07
%S A379352 0,1,3,7,6,11,16,23,20,12,9,40,17,31,26,28,51,50,18,78,34,93,15,109,
%T A379352 38,91,68,29,127,108,130,75,141,107,46,120,143,35,96,69,21,214,37,126,
%U A379352 94,67,163,56,190,261,216,153,239,207,260,104,43,288,62,206,77,262,64,151,346
%N A379352 a(n) is the smallest nonnegative integer k such the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.
%H A379352 Andrew Howroyd, <a href="/A379352/b379352.txt">Table of n, a(n) for n = 1..10000</a>
%e A379352 Table showing n, A033203(n), a(n), a(n)^2 + 2:
%e A379352    1  2  0   2
%e A379352    2  3  1   3
%e A379352    3 11  3  11
%e A379352    4 17  7  51 = 17*3
%e A379352    5 19  6  38 = 19*2
%e A379352    6 41 11 123 = 41*3
%e A379352    7 43 16 258 = 43*3*2
%e A379352    8 59 23 531 = 59*3^2
%e A379352    9 67 20 402 = 67*3*2
%e A379352   10 73 12 146 = 73*2
%e A379352   ...
%o A379352 (PARI) lista(n) = { my(L=List(),p=0); while(#L<n, p=nextprime(p+1); my(r=p%8); if(r<>5&&r<>7, my(k=0); while(vecmax(factor(k^2 + 2)[,1]) <> p, k++); listput(L,k) )); Vec(L) }
%Y A379352 Cf. A033203, A059100, A006530, A185397, A379350, A379351.
%K A379352 nonn
%O A379352 1,3
%A A379352 _Andrew Howroyd_, Dec 22 2024