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.

0, 1, 3, 7, 6, 11, 16, 23, 20, 12, 9, 40, 17, 31, 26, 28, 51, 50, 18, 78, 34, 93, 15, 109, 38, 91, 68, 29, 127, 108, 130, 75, 141, 107, 46, 120, 143, 35, 96, 69, 21, 214, 37, 126, 94, 67, 163, 56, 190, 261, 216, 153, 239, 207, 260, 104, 43, 288, 62, 206, 77, 262, 64, 151, 346

Offset: 1

Author

Andrew Howroyd, Dec 22 2024

Keywords

• nonn

Examples

			Table showing n, A033203(n), a(n), a(n)^2 + 2:
   1  2  0   2
   2  3  1   3
   3 11  3  11
   4 17  7  51 = 17*3
   5 19  6  38 = 19*2
   6 41 11 123 = 41*3
   7 43 16 258 = 43*3*2
   8 59 23 531 = 59*3^2
   9 67 20 402 = 67*3*2
  10 73 12 146 = 73*2
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033203, A059100, A006530, A185397, A379350, A379351.

Programs

PARI

lista(n) = { my(L=List(),p=0); while(#L5&&r<>7, my(k=0); while(vecmax(factor(k^2 + 2)[,1]) <> p, k++); listput(L,k) )); Vec(L) }