A191025 -id:A191025 - cp's OEIS frontend

A038889 Primes p such that 17 is a square mod p.

2, 13, 17, 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

Offset: 1

N. J. A. Sloane

nonn

Also primes of the form 2*x^2+x*y-2*y^2 (as well as of the form 2*x^2+5*x*y+y^2). Discriminant = 17. Class = 1. This was originally a separate entry, submitted by Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 06 2008. R. J. Mathar proved that this coincides with the present sequence, Jul 22 2008

Also, primes which are a square (mod 17) (or, (mod 34), cf. A191025). - M. F. Hasler, Jan 15 2016

Z. I. Borevich and I. R. Shafarevich, Number Theory.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
D. B. Zagier, Zetafunktionen und quadratische Körper, Springer, 1981.

Cf. A038889 (17 is a square mod p); A141111, A141112 (d=65).

Primes in A035258.

Select[Prime[Range[200]],JacobiSymbol[17,#]!=-1&] (* Harvey P. Dale, Sep 20 2011 *)

is(n)=isprime(n)&&issquare(Mod(17,n)) \\ Charles R Greathouse IV, Mar 21 2013

Edited by N. J. A. Sloane, Jul 28 2008 at the suggestion of R. J. Mathar

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

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

A191037 Primes p that have Jacobi symbol (p|58) = 1.

Original entry on oeis.org

3, 7, 11, 19, 23, 37, 43, 61, 71, 101, 103, 131, 151, 157, 163, 167, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 281, 293, 307, 313, 317, 331, 353, 379, 383, 389, 401, 421, 431, 439, 443, 457, 461, 463, 467, 487, 491, 521, 541, 563, 593, 619, 631, 647

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "Primes which are squares mod 58", which is sequence A038901. - 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, A191036.

[p: p in PrimesUpTo(647) | KroneckerSymbol(p, 58) eq 1]; // Vincenzo Librandi, Sep 11 2012

select(t -> isprime(t) and numtheory:-jacobi(t,58)=1, [seq(i,i=3..1000,2)]); # Robert Israel, Jan 15 2016

Select[Prime[Range[200]], JacobiSymbol[#,58]==1&]

select(p->kronecker(p,58)==1&&isprime(p),[1..1000]) \\ This is to provide a generic characteristic function ("is_A191037") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016

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

A191040 Primes p that have Kronecker symbol (p|62) = 1.

Original entry on oeis.org

3, 7, 11, 13, 29, 37, 41, 43, 47, 53, 61, 71, 83, 97, 103, 113, 139, 179, 181, 191, 193, 197, 229, 233, 251, 257, 269, 277, 281, 311, 331, 347, 359, 389, 431, 439, 461, 479, 491, 499, 503, 509, 521, 523, 557, 571, 577, 587, 593, 599, 607, 613, 617, 619, 643

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares (mod 62)", which is sequence A267481. - 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, A191036, A191037.

[p: p in PrimesUpTo(643) | KroneckerSymbol(p, 62) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,62]==1&]

select(p->kronecker(p, 62)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191040") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016

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

A191042 Primes p that have Jacobi symbol (p|69) = 1.

Original entry on oeis.org

5, 11, 13, 17, 31, 53, 73, 83, 89, 107, 113, 127, 137, 139, 149, 151, 163, 191, 193, 211, 223, 227, 251, 263, 271, 277, 281, 293, 307, 331, 349, 359, 383, 389, 397, 401, 409, 419, 431, 439, 463, 467, 479, 487, 499, 503, 521, 541, 547, 557, 563, 569, 577, 601

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares mod 69", which would be the sequence (3, 13, 31, 73, 127, 139, 151, 163, 193, 211, 223, 271, 277, 307, 331, 349, 397, ...). - 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, A191036, A191037, A191040, A191043, A191046, A191047, A191049.

[p: p in PrimesUpTo(601) | JacobiSymbol(p, 69) eq 1]; // Vincenzo Librandi, Sep 10 2012

Select[Prime[Range[200]], JacobiSymbol[#,69]==1&]

select(p->kronecker(p, 69)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191043") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016

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

cp's OEIS Frontend

A038889 Primes p such that 17 is a square mod p.

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

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

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

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