A320103 -id:A320103

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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).

+10
3

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

(list; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,hard

AUTHOR

Rémy Sigrist, Oct 01 2018

STATUS

approved

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