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

1,3

Links

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

Example

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
  ...

Prog

(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) }

Crossrefs

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

Sequence in context: A338067 A178242 A352168 * A375021 A070882 A109635

Adjacent sequences: A379349 A379350 A379351 * A379353 A379354 A379355

Keyword

nonn

Author

Andrew Howroyd, Dec 22 2024

Status

approved