A058770 - OEIS

A058770

Numbers k such that k * (1+i)^k + 1 is a Gaussian prime.

1, 2, 3, 5, 9, 19, 20, 29, 30, 68, 142, 143, 150, 159, 198, 468, 782, 858, 1100, 1137, 3337, 3638, 3909, 4845, 16895, 30349, 42692, 48470

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OFFSET

1,2

LINKS

MAPLE

select(n -> GaussInt:-GIprime(n*(1+I)^n+1), [$1..50000]); # Robert Israel, May 08 2023

MATHEMATICA

Do[ If[ PrimeQ[ n * (1 + I)^n + 1, GaussianIntegers -> True], Print[n] ], {n, 1, 4000} ]

PROG

(Python)

from itertools import count, islice

from sympy import I

from sympy.ntheory import is_gaussian_prime

def A058770_gen(startvalue=1): # generator of terms

x = (1+I)**(m:=max(startvalue, 1))

for k in count(m):

if is_gaussian_prime(k*x+1):

yield k

x *= (1+I)

A058770_list = list(islice(A058770_gen(), 20)) # Chai Wah Wu, May 09 2023

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

EXTENSIONS

Corrected by Robert Israel, May 08 2023

STATUS

approved