A308660 - OEIS

%I #12 Jun 18 2019 07:55:57

%S 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,

%T 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,

%U 19,29,23,13,3,3,5,5,3,7,15,3,25,3,7,5,3,5,3,3,3

%N 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).

%C A002145 corresponds to the natural numbers that are also Gaussian prime numbers.

%C This sequence generalizes to Gaussian integers an idea developed in A308261.

%C Visually, the connected components of G appear like constellations (see representation in Links section).

%H Rémy Sigrist, <a href="/A308660/a308660.png">Representation of the connected components of G with a term z such that 0 <= Re(z) <= 100 and 0 <= Im(z) <= 100</a>

%H Rémy Sigrist, <a href="/A308660/a308660.gp.txt">PARI program for A308660</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GaussianPrime.html">Gaussian Prime</a>

%e For n=3:

%e - A002145(3) = 11,

%e - the nearest Gaussian primes to 11 (at equal distance) are 10+i and 10-i,

%e - the other Gaussian primes around 11, 10+i and 10-i are nearer from other Gaussian primes,

%e - so the connected component containing 11 contains: 11, 10+i and 10-i,

%e - and a(3) = 3.

%o (PARI) See Links section.

%Y Cf. A002145, A308261.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Jun 15 2019