A128106 Sizes of possible gaps around a Gaussian prime: 1 and the even numbers in A001481.

1, 2, 4, 8, 10, 16, 18, 20, 26, 32, 34, 36, 40, 50, 52, 58, 64, 68, 72, 74, 80, 82, 90, 98, 100, 104, 106, 116, 122, 128, 130, 136, 144, 146, 148, 160, 162, 164, 170, 178, 180, 194, 196, 200, 202, 208, 212, 218, 226, 232, 234, 242, 244, 250, 256, 260, 272, 274

Offset: 1

Author

T. D. Noe, Feb 15 2007

Keywords

• nonn

Comments

For a given Gaussian prime u, the size of its gap is the minimum of norm(u-v) as v varies over all other Gaussian primes, where norm(a+b*i)=a^2+b^2. Only the small Gaussian primes 1+i and 2+i (and their associates and reflections) have gaps of diameter 1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A128107, A128108, A128109.

Programs

Mathematica

q=12; imax=2*q^2; lst=Select[Union[Flatten[Table[2*x^2+2*y^2, {x,0,q}, {y,0,x}]]], #<=imax&]; Join[{1},Drop[lst,1]] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)

Sage

def A128106_list(max):
    R = []; s = 1; sq = 1
    for n in (0..max//2):
        if n == s:
            sq += 1;
            s = sq*sq;
        for k in range(sq):
            if is_square(n-k*k):
                R.append(2*n)
                break
    R[0] = 1
    return R
A128106_list(274) # Peter Luschny, Jun 20 2014