A319563 - OEIS

A319563

Let f(1) = 1, f(2) = 1 + i (where i denotes the imaginary unit), and for n > 1, f(n+1) is the Gaussian integer in the first quadrant (with positive real part and nonnegative imaginary part) with least modulus and sharing a prime factor with f(n) (in case of a tie, minimize the imaginary part); a(n) = the imaginary part of f(n).

%I #8 Sep 25 2018 11:05:37

%S 0,1,0,2,1,2,4,3,1,2,0,3,0,0,1,3,6,5,2,4,4,3,4,8,5,1,2,2,0,3,6,3,4,6,

%T 1,5,7,3,5,10,7,2,4,0,6,5,6,12,7,1,2,4,7,1,4,8,2,6,9,8,1,5,10,9,4,8,3,

%U 0,9,7,0,0,0,7,6,8,2,10,5,7,14,9,2,4,1

%N Let f(1) = 1, f(2) = 1 + i (where i denotes the imaginary unit), and for n > 1, f(n+1) is the Gaussian integer in the first quadrant (with positive real part and nonnegative imaginary part) with least modulus and sharing a prime factor with f(n) (in case of a tie, minimize the imaginary part); a(n) = the imaginary part of f(n).

%C See A319561 for the square of the modulus of f and additional comments.

%H Rémy Sigrist, <a href="/A319563/b319563.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A319563/a319563.gp.txt">PARI program for A319563</a>

%o (PARI) See Links section.

%Y Cf. A319561.

%K nonn

%O 1,4

%A _Rémy Sigrist_, Sep 23 2018