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.

A106380 Imaginary parts of numbers defined in A106379.

Original entry on oeis.org

2, 1, 2, 1, 4, 6, 13, 17, 23, 20, 27, 28, 36, 51, 55, 51, 49, 47, 123, 9, 96
Offset: 1

Views

Author

Sven Simon, Apr 30 2005

Keywords

Links

Crossrefs

Cf. A106379.

Extensions

Offset corrected and a(16)-a(21) added by Amiram Eldar, Aug 16 2025

A106377 Real part of Gaussian prime numbers such that the Gaussian primorial product up to them is a Gaussian prime minus one.

Original entry on oeis.org

1, 1, 2, 3, 2, 1, 4, 2, 1, 6, 7, 1, 10, 19, 25, 5, 13
Offset: 1

Views

Author

Sven Simon, Apr 30 2005

Keywords

Comments

Consider the Gaussian primes of the first quadrant a+bi, with a > 0, b >= 0, ordered as a sequence by the size of the norm and the size of the real part a, as defined in A103431. The product of these primes up to a+bi, written here as cp#, may have the property that cp#+1 is a Gaussian prime. a(n) is the real part a of such a+bi. cp#+1 is not necessarily in the first quadrant.
From R. J. Mathar, Jun 13 2011: (Start)
Consider the partial products of the complex sequence A103431(n)+A103432(n)*i, which starts p# = 1+i, -1+3i, -5+5i, -15+15i, -75-15i, -195-195i, 585-975i, 3315-3315i, ... If 1+p# is a Gaussian prime, we insert the real part of the last factor, A103431(n), into this sequence. The first missing element is A103431(6), meaning -194-195i is not a Gaussian prime.
The 7 is for products up to norm 192, the 1 for products up to 256, the 10 for 268, 19 up to 360 and the 25 up to 820. (No further up to norm 5700. Is the sequence finite?) (End)

Examples

			(1+i)*(1+2i)*(2+i)*3*(2+3i) + 1 = (-75-15i) + 1 = (-74-15i), which is a Gaussian prime. This is the 5th number with the property, so a(5) = 2.

Links

Crossrefs

Cf. A103431, A103432, A106378, A106379, A106381, A106383.

Extensions

Offset corrected and a(16)-a(17) added by Amiram Eldar, Aug 16 2025

A106381 Real part of Gaussian prime numbers such that the Gaussian primorial product up to them is a Gaussian prime minus i.

Original entry on oeis.org

1, 1, 2, 2, 1, 6, 4, 11, 10, 11, 19, 3, 18, 16, 40, 27, 139
Offset: 1

Views

Author

Sven Simon, Apr 30 2005

Keywords

Comments

A106382 has the imaginary parts of these numbers.

Examples

			(1+i)*(1+2i)*(2+i)*3*(2+3i)*(3+2i)*(1+4i) + i = (585-975i) + i = (585-974i), which is a Gaussian prime. This is the 5th number with the property, so a(5) = 1.

Links

Crossrefs

Cf. A103431, A103432, A106377, A106379, A106382, A106384.

Extensions

a(15)-a(17) from Amiram Eldar, Aug 16 2025

A106383 Real part of Gaussian prime numbers such that the Gaussian primorial product up to them is a Gaussian prime plus i.

Original entry on oeis.org

1, 2, 3, 2, 3, 4, 2, 6, 5, 5, 5, 4, 1, 25, 20, 3, 29, 36, 74, 112, 140, 48
Offset: 1

Views

Author

Sven Simon, Apr 30 2005

Keywords

Comments

A106384 has the imaginary parts.

Examples

			(1+i)*(1+2i)*(2+i)*3*(2+3i)*(3+2i)*(1+4i)*(4+i)*(2+5i) - i = (23205+9945i) - i = (23205+9944i), which is a Gaussian prime. This is the 7th number with the property, so a(7) = 2.

Links

Crossrefs

Cf. A103431, A103432, A106377, A106379, A106381, A106384.

Extensions

a(18)-a(22) from Amiram Eldar, Aug 16 2025
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.