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A284376 a(n) is the least nonnegative integer such that n + i*a(n) is a Gaussian prime. 1
3, 1, 1, 0, 1, 2, 1, 0, 3, 4, 1, 0, 7, 2, 1, 2, 1, 2, 5, 0, 1, 4, 5, 0, 1, 4, 1, 2, 5, 4, 11, 0, 3, 2, 5, 2, 1, 2, 3, 10, 1, 4, 5, 0, 9, 2, 5, 0, 13, 4, 7, 4, 3, 10, 1, 4, 1, 2, 3, 0, 13, 10, 3, 32, 9, 2, 1, 0, 5, 10, 3, 0, 5, 2, 1, 4, 5, 10, 7, 0, 7, 4, 3, 0, 1, 2, 9, 2, 3, 4, 1, 4, 7, 8, 1, 2, 5, 2, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Lars-Erik Svahn, numbertheory.4th
Akshaa Vatwani, Bounded gaps between Gaussian primes, Journal of Number Theory, Volume 171, February 2017, Pages 449-473.
Wikipedia, Gaussian prime
FORMULA
From Michel Marcus, Mar 30 2017: (Start)
a(n) = 0 for n in A002145.
a(n) = 1 for n in A005574.
(End)
a(n) = A069003(n) if n is not in A002145. - Robert Israel, Apr 07 2017
MAPLE
f:= proc(n) local k;
for k from 0 do if GaussInt:-GIprime(n+I*k) then return k fi od
end proc:
map(f, [$0..100]); # Robert Israel, Apr 07 2017
MATHEMATICA
Table[k = 0; While[! PrimeQ[n + I k, GaussianIntegers -> True], k++]; k, {n, 0, 100}] (* Michael De Vlieger, Mar 29 2017 *)
PROG
(ANS-Forth)
s" numbertheory.4th" included
: 3mod4_prime \ n -- flag
abs dup isprime swap 3 and 3 = and ;
: isGaussianPrime \ a b -- flag
over 0= if nip 3mod4_prime exit then
dup 0= if drop 3mod4_prime exit then
dup * swap dup * + isprime ;
: Gauss_prime \ n -- a(n)
0
begin 2dup isGaussianPrime 0=
while 1+
repeat nip ;
CROSSREFS
Sequence in context: A338638 A062172 A196838 * A088205 A318923 A336111
KEYWORD
nonn
AUTHOR
Lars-Erik Svahn, Mar 25 2017
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)