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

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

Example

For n=3:
- A002145(3) = 11,
- the nearest Gaussian primes to 11 (at equal distance) are 10+i and 10-i,
- the other Gaussian primes around 11, 10+i and 10-i are nearer from other Gaussian primes,
- so the connected component containing 11 contains: 11, 10+i and 10-i,
- and a(3) = 3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A002145, A308261.

Sequence in context: A115020 A169735 A096582 * A220023 A115048 A112525

Adjacent sequences: A308657 A308658 A308659 * A308661 A308662 A308663

Keyword

nonn

Author

Rémy Sigrist, Jun 15 2019

Status

approved