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

1,2

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

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 *)

Prog

(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

Crossrefs

Cf. A128107, A128108, A128109.

Sequence in context: A341655 A171757 A350780 * A354776 A125021 A085406

Adjacent sequences: A128103 A128104 A128105 * A128107 A128108 A128109

Keyword

nonn

Author

T. D. Noe, Feb 15 2007

Status

approved