A191020 -id:A191020 - cp's OEIS frontend

A191017 Primes with Kronecker symbol (p|14) = 1.

3, 5, 13, 19, 23, 59, 61, 71, 79, 83, 101, 113, 127, 131, 137, 139, 151, 157, 173, 181, 191, 193, 227, 229, 233, 239, 251, 263, 269, 281, 283, 293, 307, 337, 349, 359, 397, 401, 419, 431, 449, 457, 461, 463, 467, 487, 509, 523, 563, 569, 587, 599, 617, 619

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "Primes that are squares mod 14", which is sequence A045373. - M. F. Hasler, Jan 15 2016
Conjecture: primes congruent to {1, 3, 5, 9, 13, 15, 19, 23, 25, 27, 39, 45} mod 56. - Vincenzo Librandi, Jun 22 2016
From Jianing Song, Nov 21 2019: (Start)
Rational primes that decompose in the field Q(sqrt(-14)).
These are primes p such that either one of (a) p == 1, 2, 4 (mod 7), p == 1, 7 (mod 8) or (b) p == 3, 5, 6 (mod 7), p == 3, 5 (mod 8) holds. So the conjecture above is correct. (End)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191018, A191020, A191061, A274504.

[p: p in PrimesUpTo(619) | KroneckerSymbol(p, 14) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,14]==1&]

is(p)=kronecker(p, 14)==1&&isprime(p) \\ Michel Marcus, Jun 23 2016 after A191032

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191023 Primes p which have Kronecker symbol (p|30) = 1.

Original entry on oeis.org

11, 13, 17, 23, 29, 31, 37, 43, 47, 59, 67, 79, 101, 113, 131, 137, 149, 151, 157, 163, 167, 179, 199, 233, 241, 251, 257, 263, 269, 271, 277, 283, 307, 353, 373, 383, 389, 397, 409, 419, 439, 461, 491, 503, 509, 523, 547, 593, 601, 613, 617, 631, 643, 647

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 30)", which is sequence A033212. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020.

[p: p in PrimesUpTo(647) | KroneckerSymbol(p, 30) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,30]==1&]

is(n)=isprime(n) && kronecker(n,30)==1 \\ Charles R Greathouse IV, Jul 12 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191025 Primes p which have Kronecker symbol (p|34) = 1.

Original entry on oeis.org

3, 5, 11, 29, 37, 47, 61, 89, 103, 107, 109, 127, 131, 137, 139, 151, 163, 173, 181, 191, 197, 211, 223, 227, 239, 257, 263, 269, 271, 277, 281, 283, 317, 347, 353, 359, 379, 383, 397, 409, 419, 433, 457, 463, 499, 541, 547, 569, 571, 577, 593, 599, 619, 631

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 34)", which is sequence A038889. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023.

[p: p in PrimesUpTo(631) | KroneckerSymbol(p, 34) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,34]==1&]

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191026 Primes p that have Jacobi symbol (p|35) = 1.

Original entry on oeis.org

3, 11, 13, 17, 29, 47, 71, 73, 79, 83, 97, 103, 109, 149, 151, 157, 167, 173, 179, 191, 211, 223, 227, 239, 257, 281, 283, 293, 307, 313, 331, 353, 359, 367, 379, 383, 389, 397, 401, 421, 431, 433, 449, 467, 491, 499, 503, 523, 541, 563, 569, 571, 577, 587

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "Primes which are squares (mod 35)", which is subsequence A106881. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025.

[p: p in PrimesUpTo(587) | JacobiSymbol(p,35) eq 1]; // Vincenzo Librandi, Sep 10 2012

Select[Prime[Range[200]], JacobiSymbol[#,35]==1&]

is(p)=kronecker(p, 35)==1&&isprime(p) \\ M. F. Hasler, Jan 15 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191028 Primes p with Kronecker symbol (p|38) = 1.

Original entry on oeis.org

3, 7, 13, 17, 23, 29, 37, 47, 53, 59, 67, 73, 107, 109, 137, 173, 179, 181, 191, 199, 211, 227, 233, 239, 263, 269, 271, 293, 307, 311, 313, 317, 331, 353, 359, 367, 373, 379, 421, 457, 463, 479, 503, 509, 523, 547, 563, 577, 593, 617, 631, 647, 659, 661

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 38)", which is sequence A106863. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025, A191026.

[p: p in PrimesUpTo(661) | KroneckerSymbol(p, 38) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,38]==1&]

is(p)=kronecker(p, 38)==1&&isprime(p) \\ M. F. Hasler, Jan 15 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191029 Primes p with Jacobi symbol (p|39) = 1.

Original entry on oeis.org

2, 5, 11, 41, 43, 47, 59, 61, 71, 79, 83, 89, 103, 127, 137, 139, 149, 157, 167, 181, 197, 199, 211, 227, 239, 277, 281, 283, 293, 313, 317, 337, 353, 359, 367, 373, 383, 401, 431, 433, 439, 449, 461, 479, 509, 523, 547, 557, 571, 587, 593, 601, 607, 617

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 39)", which is subsequence A267455 \ {3, 13}. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025, A191026, A191028.

[p: p in PrimesUpTo(617) | JacobiSymbol(p, 39) eq 1]; // Vincenzo Librandi, Sep 10 2012

Select[Prime[Range[200]], JacobiSymbol[#,39]==1&]

select(p->kronecker(p,39)==1&&isprime(p),[1..1000]) \\ M. F. Hasler, Jan 15 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A056874 Primes of form x^2+xy+3y^2, discriminant -11.

Original entry on oeis.org

3, 5, 11, 23, 31, 37, 47, 53, 59, 67, 71, 89, 97, 103, 113, 137, 157, 163, 179, 181, 191, 199, 223, 229, 251, 257, 269, 311, 313, 317, 331, 353, 367, 379, 383, 389, 397, 401, 419, 421, 433, 443, 449, 463, 467, 487, 499, 509, 521, 577, 587, 599

Offset: 1

N. J. A. Sloane, Sep 02 2000

Also, primes of form (x^2+11*y^2)/4.
Also, primes of the form x^2-xy+3y^2 with x and y nonnegative. - T. D. Noe, May 07 2005
Primes congruent to 0, 1, 3, 4, 5 or 9 (mod 11). As this discriminant has class number 1, all binary quadratic forms ax^2+bxy+cy^2 with b^2-4ac=-11 represent these primes. - Rick L. Shepherd, Jul 25 2014
Also, primes which are squares (mod 11) (or, (mod 22), cf. A191020). - M. F. Hasler, Jan 15 2016
Also, primes p such that Legendre(-11,p) = 0 or 1. - N. J. A. Sloane, Dec 25 2017

Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 4000 terms from N. J. A. Sloane]
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Cf. A002346 and A002347 for values of x and y.

Primes in A028954.

QuadPrimes2[1, 1, 3, 100000] (* see A106856 *)

{ fc2(a,b,c,M) = my(p,t1,t2,n);
m = 0;
for(n=1,M, p = prime(n);
t2 = qfbsolve(Qfb(a,b,c),p); if(t2 == 0,, m++; print(m," ",p )));
}
fc2(1,-1,3,10703);

Edited by N. J. A. Sloane, Jun 01 2014 and Jun 16 2014

A191032 Primes p with Kronecker symbol (p|46) = 1.

Original entry on oeis.org

5, 11, 19, 31, 37, 41, 43, 47, 53, 61, 67, 71, 73, 83, 107, 109, 127, 149, 151, 157, 167, 181, 193, 223, 227, 229, 233, 239, 251, 257, 271, 283, 293, 311, 353, 373, 379, 389, 409, 419, 421, 439, 449, 463, 467, 487, 523, 557, 563, 571, 577, 593, 599, 601, 607

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 46)". - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025, A191026, A191028, A191029.

[p: p in PrimesUpTo(607) | KroneckerSymbol(p, 46) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,46]==1&]

select(p->kronecker(p,46)==1&&isprime(p),[1..1000]) \\ M. F. Hasler, Jan 15 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191036 Primes p that have Jacobi symbol (p|55) = 1.

Original entry on oeis.org

2, 7, 13, 17, 31, 43, 59, 71, 73, 83, 89, 107, 127, 167, 173, 179, 181, 191, 193, 197, 199, 227, 229, 233, 251, 263, 269, 277, 283, 293, 307, 311, 331, 337, 347, 373, 379, 389, 401, 419, 421, 449, 457, 499, 503, 509, 521, 523, 547, 557, 563, 593, 599, 607

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares mod 55", which is sequence A267478, a subsequence whose terms have (p|5) = (p|11) = 1 except for the two initial terms 5 and 11. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025, A191026, A191028, A191029,A191032, A191034, A191037.

[p: p in PrimesUpTo(607) | JacobiSymbol(p, 55) eq 1]; // Vincenzo Librandi, Sep 10 2012

Select[Prime[Range[200]], JacobiSymbol[#,55]==1&]

select(p->kronecker(p,55)==1&&isprime(p),[1..1500]) \\ M. F. Hasler, Jan 15 2016

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

A191034 Primes p with Jacobi symbol (p|51) = 1.

Original entry on oeis.org

5, 11, 13, 19, 23, 29, 41, 43, 67, 71, 103, 107, 113, 127, 131, 151, 157, 167, 173, 197, 223, 227, 229, 233, 269, 271, 307, 311, 317, 331, 347, 349, 373, 401, 409, 419, 421, 431, 433, 449, 457, 463, 479, 503, 521, 523, 577, 613, 617, 631, 641, 653, 661, 677

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 51)", which is subsequence A106904. - M. F. Hasler, Jan 15 2016

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A191017, A191018, A191020, A191023, A191025, A191026, A191028, A191029, A191032, A191036, A191037.

[p: p in PrimesUpTo(677) | JacobiSymbol(p, 51) eq 1]; // Vincenzo Librandi, Sep 10 2012

Select[Prime[Range[200]], JacobiSymbol[#,51]==1&]

Definition corrected (following an observation by David Broadhurst) by M. F. Hasler, Jan 15 2016

cp's OEIS Frontend

A191017 Primes with Kronecker symbol (p|14) = 1.

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A191023 Primes p which have Kronecker symbol (p|30) = 1.

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A191025 Primes p which have Kronecker symbol (p|34) = 1.

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A191026 Primes p that have Jacobi symbol (p|35) = 1.

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A191028 Primes p with Kronecker symbol (p|38) = 1.

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A191029 Primes p with Jacobi symbol (p|39) = 1.

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A056874 Primes of form x^2+xy+3y^2, discriminant -11.

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