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

1,1

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

Table of n, a(n) for n=1..26.

Rémy Sigrist, PARI program for A319920

Formula

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A000945, A055025, A320103, A320104.

Sequence in context: A139023 A241758 A173620 * A166134 A336883 A067365

Adjacent sequences: A319917 A319918 A319919 * A319921 A319922 A319923

Keyword

nonn,hard

Author

Rémy Sigrist, Oct 01 2018

Status

approved