The On-Line Encyclopedia of Integer Sequences (OEIS)

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Revision History for A319920

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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).
(history; published version)

#9 by Susanna Cuyler at Mon Oct 08 08:07:27 EDT 2018

STATUS

proposed

approved

#8 by Rémy Sigrist at Mon Oct 08 04:08:59 EDT 2018

STATUS

editing

proposed

#7 by Rémy Sigrist at Sat Oct 06 09:15:20 EDT 2018

LINKS

Rémy Sigrist, <a href="/A319920/a319920.gp.txt">TITLE FOR LINKPARI program for A319920</a>

#6 by Rémy Sigrist at Sat Oct 06 09:14:59 EDT 2018

LINKS

Rémy Sigrist, <a href="/A319920/a319920.gp.txt">TITLE FOR LINK</a>

PROG

(PARI) See Links section.

#5 by Rémy Sigrist at Sat Oct 06 06:17:51 EDT 2018

FORMULA

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

#4 by Rémy Sigrist at Sat Oct 06 06:17:23 EDT 2018

COMMENTS

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

FORMULA

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

CROSSREFS

Cf. A000945, A055025, A320103, A320104.

#3 by Rémy Sigrist at Mon Oct 01 13:54:59 EDT 2018

NAME

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 by Rémy Sigrist at Mon Oct 01 13:51:27 EDT 2018

NAME

allocated Let f(1) = 1 + i (where i denotes the imaginary unit) and for Rémy Sigristn > 0, f(n+1) is the Gaussian prime 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).

DATA

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

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

All terms belong to A055025.

CROSSREFS

Cf. A000945, A055025.

KEYWORD

allocated

nonn,hard

AUTHOR

Rémy Sigrist, Oct 01 2018

STATUS

approved

editing

#1 by Rémy Sigrist at Mon Oct 01 13:51:27 EDT 2018

NAME

allocated for Rémy Sigrist

KEYWORD

allocated

STATUS

approved