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A128106 Sizes of possible gaps around a Gaussian prime: 1 and the even numbers in A001481. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A076919 A336659 A171757 * A125021 A085406 A022340

Adjacent sequences:  A128103 A128104 A128105 * A128107 A128108 A128109

KEYWORD

nonn

AUTHOR

T. D. Noe, Feb 15 2007

STATUS

approved

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Last modified August 10 02:28 EDT 2020. Contains 336367 sequences. (Running on oeis4.)