A128109 -id:A128109 - cp's OEIS frontend

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

T. D. Noe, Feb 15 2007

nonn

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.

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

Cf. A128107, A128108, A128109.

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 *)

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

A128107 Real part of the smallest Gaussian prime having a gap size of exactly A128106(n).

Original entry on oeis.org

1, 3, 17, 23, 46, 79, 235, 221, 427, 1024, 563, 1753, 1837, 3664, 4411, 18307, 14243

Offset: 1

T. D. Noe, Feb 15 2007

nonn

Due to symmetry, there are actually 4 or 8 Gaussian primes having this gap size. We list the prime in the first octant of the complex plane.

Cf. A128108, A128109.

A128108 Imaginary part of the smallest Gaussian prime having a gap size of exactly A128106(n).

Original entry on oeis.org

1, 0, 12, 8, 5, 0, 48, 24, 320, 281, 0, 1688, 632, 2951, 3914, 2752, 0

Offset: 1

T. D. Noe, Feb 15 2007

nonn

Due to symmetry, there are actually 4 or 8 Gaussian primes having this gap size. We list the prime in the first octant of the complex plane.

Cf. A128107, A128109.

cp's OEIS Frontend

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

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A128107 Real part of the smallest Gaussian prime having a gap size of exactly A128106(n).

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A128108 Imaginary part of the smallest Gaussian prime having a gap size of exactly A128106(n).

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Author

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