A319920 Let f(1) = 1 + i (where i denotes the imaginary unit) and for n > 0, f(n+1) is the Gaussian prime in the first quadrant (with positive real part and nonnegative imaginary part) with least modulus that divides 1 + Product_{k=1..n} f(k) (in case of a tie minimize the imaginary part); a(n) is the square of the modulus of f(n).

2, 5, 13, 9, 1129, 29, 17, 651250309, 5, 13, 17, 29, 37, 16767128453, 41, 133981, 2236369, 61, 45293, 22481146745713207066897, 12041, 653, 51908348513173, 121, 11821, 779353

Offset: 1

Author

Rémy Sigrist, Oct 01 2018

Keywords

• nonn
• hard

Comments

The real and imaginary parts of f are respectively given by A320103 and A320104.

This sequence is a complex variant of the Euclid-Mullin sequence (A000945).

All terms belong to A055025.

Links

• Rémy Sigrist, PARI program for A319920

Crossrefs

Cf. A000945, A055025, A320103, A320104.

Programs

PARI

See Links section.

Formula

a(n) = A320103(n)^2 + A320104(n)^2.