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 21-28 of 28 results.

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

A297175 Rational primes that decompose in the field Q(sqrt(19)).

Original entry on oeis.org

3, 5, 17, 31, 59, 61, 67, 71, 73, 79, 101, 103, 107, 127, 137, 149, 151, 157, 167, 179, 197, 211, 223, 227, 229, 233, 277, 307, 313, 331, 349, 353, 379, 383, 389, 397, 431, 439, 457, 461, 487, 523, 541, 547, 557, 563, 577, 593, 599, 607, 613, 617, 653
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Crossrefs

Cf. A297176, A038891, A038892.

Programs

A297176 Inert rational primes in the field Q(sqrt(19)).

Original entry on oeis.org

7, 11, 13, 23, 29, 37, 41, 43, 47, 53, 83, 89, 97, 109, 113, 131, 139, 163, 173, 181, 191, 193, 199, 239, 241, 251, 257, 263, 269, 271, 281, 283, 293, 311, 317, 337, 347, 359, 367, 373, 401, 409, 419, 421, 433, 443, 449, 463, 467, 479, 491, 499, 503, 509, 521, 569
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Crossrefs

Cf. A038892.

Programs

A296924 Primes p such that Legendre(-6,p) = 0 or 1.

Original entry on oeis.org

2, 3, 5, 7, 11, 29, 31, 53, 59, 73, 79, 83, 97, 101, 103, 107, 127, 131, 149, 151, 173, 179, 193, 197, 199, 223, 227, 241, 251, 269, 271, 293, 313, 317, 337, 347, 367, 389, 409, 419, 433, 439, 443, 457, 461, 463, 467, 487, 491, 509, 557, 563, 577, 587, 601, 607, 631, 653, 659, 673, 677, 683
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Comments

Primes == 1, 2, 3, 5, 7, or 11 (mod 24). - Robert Israel, Dec 27 2017

Links

Crossrefs

Cf. A157437, A191059.

Programs

  • Maple
    Load the Maple program HH given in A296920. Then run HH(-6, 200); This produces A157437, A191059, and the present sequence.
select(isprime, {seq(seq(24*i+j,j=[1,2,3,5,7,11]),i=0..100)});

A296932 Primes p such that Legendre(-23,p) = 0 or 1.

Original entry on oeis.org

2, 3, 13, 23, 29, 31, 41, 47, 59, 71, 73, 101, 127, 131, 139, 151, 163, 167, 173, 179, 193, 197, 211, 223, 233, 239, 257, 269, 271, 277, 307, 311, 317, 331, 347, 349, 353, 397, 409, 439, 443, 449, 461, 463, 487, 491, 499, 509, 541, 547, 577, 587
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Comments

Primes == 0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 16, or 18 (mod 23). - Robert Israel, Dec 26 2017

Links

Programs

  • Maple
    Load the Maple program HH given in A296920. Then run HH(-23, 200); This produces A191021, A191065, A296932.
Alternative:
select(isprime, [2,seq(seq(46*i+j,j=[1, 3, 9, 13, 23, 25, 27, 29, 31, 35, 39, 41]),i=0..30)]); # Robert Israel, Dec 26 2017

A296934 Rational primes that decompose in the field Q(sqrt(7)).

Original entry on oeis.org

3, 19, 29, 31, 37, 47, 53, 59, 83, 103, 109, 113, 131, 137, 139, 149, 167, 193, 197, 199, 223, 227, 233, 251, 271, 277, 281, 283, 307, 311, 317, 337, 367, 373, 383, 389, 401, 419, 421, 439, 449, 457, 467, 479, 503, 523, 541, 557, 563, 569, 587, 607, 613
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Programs

A297177 Rational primes that decompose in the field Q(sqrt(23)).

Original entry on oeis.org

7, 11, 13, 19, 29, 41, 43, 67, 73, 79, 83, 101, 103, 107, 173, 191, 193, 197, 199, 227, 233, 251, 257, 263, 269, 277, 283, 317, 349, 353, 359, 367, 379, 383, 397, 409, 419, 431, 449, 461, 467, 479, 503, 509, 523, 541, 563, 571, 577, 593, 601, 619, 631
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Programs

A296933 Primes p such that Legendre(3,p) = 0 or 1.

Original entry on oeis.org

3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193, 227, 229, 239, 241, 251, 263, 277, 311, 313, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 431, 433, 443, 457, 467, 479, 491, 503, 541, 563, 577
Offset: 1

Views

Author

N. J. A. Sloane, Dec 26 2017

Keywords

Links

Crossrefs

This is A038874 without the initial 2.
Cf. A003630, A038875, A097933, A296920.

Programs

  • Maple
    # Load the Maple program HH given in A296920. Then run HH(3, 200); This produces A097933, A003630, this sequence, and A038875.
  • Mathematica
    Join[{3}, Select[Prime[Range[200]], JacobiSymbol[3, #] == 1 &]] (* Paolo Xausa, May 11 2024 *)
Previous Showing 21-28 of 28 results.

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

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