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.

Previous Showing 11-14 of 14 results.

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

A190634 Indices of primes from A190637.

Original entry on oeis.org

2, 14, 969, 2831, 4050, 6167
Offset: 1

Views

Author

Sven Simon, May 15 2011

Keywords

Comments

See A190637.

Crossrefs

Cf. A103431 (Gaussian primes in first quadrant), A190635 (index of same prime as Gaussian prime), A190637 (primes == 3 mod 4).

Extensions

a(5)-a(6) from Sven Simon, Jun 19 2011

A262433 Quater-imaginary representation of the Gaussian primes with an even imaginary part.

Original entry on oeis.org

3, 11, 13, 21, 31, 101, 111, 113, 123, 133, 201, 211, 213, 223, 233, 301, 321, 323, 331, 1003, 1011, 1021, 1031, 1033, 1101, 1113, 1123, 1131, 1133, 1201, 1203, 1213, 1223, 1231, 1233, 1311, 1321, 1323, 2001, 2011, 2031, 2033, 2103, 2113, 2131, 2133, 2203
Offset: 1

Views

Author

Adam J.T. Partridge, Sep 22 2015

Keywords

Comments

Not all Gaussian primes will be in this list as complex numbers with an odd imaginary part require a value after the radix point (".") in the quater-imaginary number system.

Examples

			1231_(2i) = 1(2i)^3 + 2(2i)^2 + 3(2i)^1 + 1(2i)^0 = -7-2i which is a Gaussian prime.

Links

Crossrefs

A002145 when translated using A212494 is a subsequence.
Real and imaginary parts of the Gaussian primes A103431, A103432.
Previous Showing 11-14 of 14 results.

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

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