A191017 -id:A191017 - cp's OEIS frontend

A191020 Primes p with Kronecker symbol (p|2*11) = 1.

13, 19, 23, 29, 31, 43, 47, 61, 71, 83, 89, 97, 101, 103, 107, 109, 113, 131, 137, 139, 149, 173, 191, 197, 199, 211, 223, 227, 257, 277, 283, 293, 307, 311, 313, 347, 349, 353, 367, 373, 383, 401, 433, 449, 461, 463, 487, 491, 521, 523, 541, 547, 557, 563

Offset: 1

T. D. Noe, May 24 2011

Originally incorrectly named "primes which are squares (mod 22)", which is sequence A056874. - M. F. Hasler, Jan 15 2016

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Cf. A191017, A191018, A191023.

[p: p in PrimesUpTo(563) | KroneckerSymbol(p, 22) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,22]==1&]

lista(nn) = forprime(p=13, nn, if(kronecker(p, 22)==1, print1(p, ", "))) \\ Iain Fox, Mar 05 2018

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

A045373 Primes congruent to {0, 1, 2, 4} mod 7.

Original entry on oeis.org

2, 7, 11, 23, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 317, 331, 337, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487

Offset: 1

N. J. A. Sloane

nonn

Primes of the form x^2 + xy + 2y^2, discriminant -7. - N. J. A. Sloane, Jun 01 2014
Primes of the form x^2 - xy + 2y^2 with x and y nonnegative. - T. D. Noe, May 07 2005
Also, primes which are squares (mod 7) (or, (mod 14): see A191017 for a sequence formerly defined as such). - M. F. Hasler, Jan 15 2016

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)

Primes in A028951.

Cf. A191017, A003625 (complement).

[p: p in PrimesUpTo(740)|p mod 7 in [0, 1, 2, 4]]; // Vincenzo Librandi, Jul 13 2012

Select[Prime[Range[500]],MemberQ[{0,1,2,4},Mod[#,7]]&] (* Vincenzo Librandi, Jul 13 2012 *)

select(p->issquare(Mod(p,7))&&isprime(p),[1..1000]) \\ 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

cp's OEIS Frontend

A191020 Primes p with Kronecker symbol (p|2*11) = 1.

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Magma

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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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Magma

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A045373 Primes congruent to {0, 1, 2, 4} mod 7.

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