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 1-3 of 3 results.

A296937 Rational primes that decompose in the field Q(sqrt(13)).

Original entry on oeis.org

3, 17, 23, 29, 43, 53, 61, 79, 101, 103, 107, 113, 127, 131, 139, 157, 173, 179, 181, 191, 199, 211, 233, 251, 257, 263, 269, 277, 283, 311, 313, 337, 347, 367, 373, 389, 419, 433, 439, 443, 467, 491, 503, 521, 523, 547, 563, 569, 571, 599, 601, 607, 641
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Comments

Is this the same sequence as A141188 or A038883? - R. J. Mathar, Jan 02 2018
From Jianing Song, Apr 21 2022: (Start)
Primes p such that Kronecker(13, p) = Kronecker(p, 13) = 1, where Kronecker() is the Kronecker symbol. That is to say, primes p that are quadratic residues modulo 13.
Primes p such that p^6 == 1 (mod 13).
Primes p == 1, 3, 4, 9, 10, 12 (mod 13). (End)

Links

Crossrefs

Cf. A011583 (kronecker symbol modulo 13), A038883.
Rational primes that decompose in the quadratic field with discriminant D: A139513 (D=-20), A191019 (D=-19), A191018 (D=-15), A296920 (D=-11), A033200 (D=-8), A045386 (D=-7), A002144 (D=-4), A002476 (D=-3), A045468 (D=5), A001132 (D=8), A097933 (D=12), this sequence (D=13), A296938 (D=17).
Cf. A038884 (inert rational primes in the field Q(sqrt(13))).

Programs

Formula

Equals A038883 \ {13}. - Jianing Song, Apr 21 2022

A296938 Rational primes that decompose in the field Q(sqrt(17)).

Original entry on oeis.org

2, 13, 19, 43, 47, 53, 59, 67, 83, 89, 101, 103, 127, 137, 149, 151, 157, 179, 191, 223, 229, 239, 251, 257, 263, 271, 281, 293, 307, 331, 349, 353, 359, 373, 383, 389, 409, 421, 433, 443, 457, 461, 463, 467, 491, 509, 523, 557, 563, 569, 577, 587, 593, 599
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Comments

From Jianing Song, Apr 21 2022: (Start)
Primes p such that kronecker(17, p) = kronecker(p, 17) = 1, where kronecker() is the kronecker symbol. That is to say, primes p that are quadratic residues modulo 17.
Primes p such that p^8 == 1 (mod 17).
Primes p == 1, 2, 4, 8, 9, 13, 15, 16 (mod 17). (End)

Links

Crossrefs

Cf. A011584 (kronecker symbol modulo 17).
Rational primes that decompose in the quadratic field with discriminant D: A139513 (D=-20), A191019 (D=-19), A191018 (D=-15), A296920 (D=-11), A033200 (D=-8), A045386 (D=-7), A002144 (D=-4), A002476 (D=-3), A045468 (D=5), A001132 (D=8), A097933 (D=12), A296937 (D=13), this sequence (D=17).
Cf. A038890 (inert rational primes in the field Q(sqrt(17))).

Programs

A247979 Numbers of the form x^2 + 7y^2 with x, y integers, or x^2/4 + 7y^2/4 with x, y odd integers.

Original entry on oeis.org

0, 1, 2, 4, 7, 8, 9, 11, 14, 16, 18, 21, 22, 23, 25, 28, 29, 32, 36, 37, 43, 44, 46, 49, 50, 53, 56, 58, 63, 64, 67, 71, 72, 74, 77, 79, 81, 86, 88, 92, 98, 99, 100, 106, 107, 109, 112, 113, 116, 121, 126, 127, 128, 134, 137, 142, 144, 148, 149, 151, 154, 158, 161, 162, 163, 169, 172
Offset: 1

Views

Author

Alonso del Arte, Sep 28 2014

Keywords

Comments

Norms of numbers in O_Q(sqrt(-7)).
A033207 and A045386 are subsets of this sequence. - Colin Barker, Sep 29 2014

Examples

			1/4 + 7/4 = 2, so 2 is in the sequence. (This also means 2 is composite in O_Q(sqrt(-7))).
2^2 + 7 * 0^2 = 4, so 4 is in the sequence.
There is no way to express 5 as x^2 + 7y^2, nor as x^2/4 + 7y^2/4 if x and y are constrained to odd integers, hence 5 is not in the sequence. (This also means 5 is prime in O_Q(sqrt(-7)) and its norm is 25).

Crossrefs

Cf. A002481, A033207, A045386.
Showing 1-3 of 3 results.

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

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