A308660 - OEIS

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).

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

Table of n, a(n) for n=1..77.

Rémy Sigrist, Representation of the connected components of G with a term z such that 0 <= Re(z) <= 100 and 0 <= Im(z) <= 100

Rémy Sigrist, PARI program for A308660

Eric Weisstein's World of Mathematics, Gaussian Prime