A319920 - OEIS

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

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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.