

A308660


For any Gaussian integer z, let d(z) be the distance from z to the nearest Gaussian prime distinct from z; we build an undirected graph G on top of the Gaussian prime numbers as follows: two Gaussian prime numbers p and q are connected iff at least one of d(p) or d(q) equals the distance from p to q; a(n) is the number of elements in the connected component of G containing A002145(n).


1



100, 100, 3, 3, 3, 15, 48, 48, 9, 19, 5, 18, 18, 3, 17, 7, 41, 7, 17, 3, 3, 3, 9, 31, 3, 6, 6, 3, 11, 33, 3, 3, 9, 5, 13, 3, 15, 7, 23, 7, 3, 3, 3, 3, 5, 3, 13, 3, 3, 5, 11, 15, 3, 9, 3, 25, 19, 29, 23, 13, 3, 3, 5, 5, 3, 7, 15, 3, 25, 3, 7, 5, 3, 5, 3, 3, 3
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OFFSET

1,1


COMMENTS

A002145 corresponds to the natural numbers that are also Gaussian prime numbers.
This sequence generalizes to Gaussian integers an idea developed in A308261.
Visually, the connected components of G appear like constellations (see representation in Links section).


LINKS



EXAMPLE

For n=3:
 the nearest Gaussian primes to 11 (at equal distance) are 10+i and 10i,
 the other Gaussian primes around 11, 10+i and 10i are nearer from other Gaussian primes,
 so the connected component containing 11 contains: 11, 10+i and 10i,
 and a(3) = 3.


PROG

(PARI) See Links section.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



