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.

A218859 A218858/4.

Original entry on oeis.org

0, 0, 1, 3, 0, 4, 0, 5, 0, 4, 0, 7, 0, 6, 0, 8, 0, 8, 0, 9, 0, 6, 0, 9, 0, 16, 0, 8, 0, 12, 0, 11, 0, 8, 0, 18, 0, 16, 0, 12, 0, 18, 0, 15, 0, 14, 0, 15, 0, 10, 0, 14, 0, 18, 0, 28, 0, 16, 0, 19, 0, 22, 0, 14, 0, 34, 0, 23, 0, 20, 0, 19, 0, 22, 0, 18, 0, 16, 0
Offset: 0

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Author

T. D. Noe, Nov 12 2012

Keywords

Comments

Essentially the number of first-quadrant Gaussian primes at taxicab distance n.

Crossrefs

Cf. A222593 (first-quadrant Gaussian primes).

A222593 Pairs of numbers (a,b) such that a + b*I is a first-quadrant Gaussian prime, ordered by a+b and then a.

Original entry on oeis.org

1, 1, 0, 3, 1, 2, 2, 1, 3, 0, 1, 4, 2, 3, 3, 2, 4, 1, 0, 7, 1, 6, 2, 5, 5, 2, 6, 1, 7, 0, 2, 7, 4, 5, 5, 4, 7, 2, 0, 11, 1, 10, 3, 8, 5, 6, 6, 5, 8, 3, 10, 1, 11, 0, 3, 10, 4, 9, 5, 8, 8, 5, 9, 4, 10, 3, 1, 14, 2, 13, 4, 11, 7, 8, 8, 7, 11, 4, 13, 2, 14, 1
Offset: 1

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Author

T. D. Noe, Feb 27 2013

Keywords

Comments

Gaussian primes on the positive real and imaginary axes are included. Note that the primes are ordered by their taxicab distance from the origin.

Crossrefs

Cf. A218858, A218859 (number of Gaussian primes at taxicab distance n).

Programs

  • Mathematica
    nn = 20; t = {}; Do[If[PrimeQ[i + (j - i) I, GaussianIntegers -> True], AppendTo[t, {i, j-i}]], {j, 0, nn}, {i, 0, j}]; Flatten[t]

A225071 Number of Gaussian primes at taxicab distance 2n-1 from the origin.

Original entry on oeis.org

0, 12, 16, 20, 16, 28, 24, 32, 32, 36, 24, 36, 64, 32, 48, 44, 32, 72, 64, 48, 72, 60, 56, 60, 40, 56, 72, 112, 64, 76, 88, 56, 136, 92, 80, 76, 88, 72, 64, 108, 72, 124, 160, 88, 112, 104, 64, 144, 112, 80, 144, 132, 80, 140, 128, 104, 160, 160, 104, 112, 136
Offset: 1

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Author

T. D. Noe, May 03 2013

Keywords

Comments

Except for 1+I, 1-I, -1+I, and -1-I, all Gaussian primes are an odd taxicab distance from the origin.

Crossrefs

Cf. A218858.

Programs

  • Mathematica
    Table[cnt = 0; Do[If[PrimeQ[n - i + I*i, GaussianIntegers -> True], cnt++], {i, 0, n}]; Do[If[PrimeQ[i - n + I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 0, -1}]; Do[If[PrimeQ[i - n - I*i, GaussianIntegers -> True], cnt++], {i, 1, n}]; Do[If[PrimeQ[n - i - I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 1, -1}]; cnt, {n, 1, 200, 2}]

A225072 Number of first-quadrant Gaussian primes at taxicab distance 2n-1 from the origin.

Original entry on oeis.org

0, 3, 4, 5, 4, 7, 6, 8, 8, 9, 6, 9, 16, 8, 12, 11, 8, 18, 16, 12, 18, 15, 14, 15, 10, 14, 18, 28, 16, 19, 22, 14, 34, 23, 20, 19, 22, 18, 16, 27, 18, 31, 40, 22, 28, 26, 16, 36, 28, 20, 36, 33, 20, 35, 32, 26, 40, 40, 26, 28, 34, 24, 46, 37, 28, 45, 30, 34, 36
Offset: 1

Views

Author

T. D. Noe, May 03 2013

Keywords

Comments

Except for 1+I, 1-I, -1+I, and -1-I, all Gaussian primes are an odd taxicab distance from the origin. Primes on the x- and y-axis are counted only once. That is, although p and p*I are Gaussian primes (for primes p in A002145), we count only p as being a first-quadrant Gaussian prime.

Crossrefs

Programs

  • Mathematica
    Table[cnt = 0; Do[If[PrimeQ[n - i + I*i, GaussianIntegers -> True], cnt++], {i, 0, n}]; Do[If[PrimeQ[i - n + I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 0, -1}]; Do[If[PrimeQ[i - n - I*i, GaussianIntegers -> True], cnt++], {i, 1, n}]; Do[If[PrimeQ[n - i - I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 1, -1}]; cnt, {n, 1, 200, 2}]/4
Showing 1-4 of 4 results.