cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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

Views

Author

T. D. Noe, Feb 15 2007

Keywords

Comments

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.

Crossrefs

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

Views

Author

T. D. Noe, Feb 15 2007

Keywords

Comments

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.

Crossrefs

Cf. A128107, A128109.

A128109 Smallest positive real Gaussian prime having a gap size of exactly A128106(n).

Original entry on oeis.org

3, 47, 31, 107, 79, 2447, 523, 1019, 11311, 563, 13411, 7559, 24943, 46867, 72103, 14243, 35759, 110339, 112967, 106591, 50023, 275323, 69991, 189251, 1267907, 849143, 1446719, 2382979, 3922691, 3166679, 6130459, 959207, 4100479, 10134671
Offset: 2

Views

Author

T. D. Noe, Feb 15 2007

Keywords

Comments

These Gaussian primes have the form p+0*i, where p is an ordinary (rational) prime with p=3 (mod 4). Gethner et al. consider gaps around real Gaussian primes. In general, the Gaussian primes whose real and imaginary parts are given in A128107 and A128108 have a smaller magnitude than the real Gaussian primes given here. However, these real Gaussian primes are easier to compute.

Links

A354776 Even numbers that are the sum of two squares; also numbers which are twice the sum of two squares.

Original entry on oeis.org

0, 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, 288, 290, 292, 296, 298, 306, 314, 320
Offset: 1

Views

Author

N. J. A. Sloane, Jun 26 2022, following a suggestion from Charles Kusniec

Keywords

Comments

This is both the even subsequence of A001481, and twice A001481. It is an easy exercise to show that these two definitions produce the same sequence.

Crossrefs

Cf. A001481. Essentially the same as A128106.

Programs

  • Python
    from itertools import count, islice
from sympy import factorint
def A354776_gen(): # generator of terms
    return filter(lambda n:(lambda m:all(d & 3 != 3 or m[d] & 1 == 0 for d in m))(factorint(n//2)),count(0,2))
A354776_list = list(islice(A354776_gen(),30)) # Chai Wah Wu, Jun 27 2022
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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