A191029 -id:A191029 - cp's OEIS frontend

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

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

A191043 Primes p that have Kronecker symbol (p|70) = 1.

Original entry on oeis.org

17, 19, 37, 43, 47, 53, 59, 61, 67, 71, 73, 79, 97, 101, 103, 107, 131, 139, 151, 163, 167, 181, 191, 197, 223, 229, 239, 251, 257, 269, 277, 281, 313, 317, 347, 349, 353, 359, 367, 373, 383, 401, 419, 431, 433, 443, 449, 461, 503, 509, 547, 557, 569, 577

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares mod 70", which is sequence A106881. - 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, A191042.

[p: p in PrimesUpTo(577) | KroneckerSymbol(p, 70) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,70]==1&]

select(p->kronecker(p, 70)==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

A191046 Primes p that have Kronecker symbol (p|74) = 1.

Original entry on oeis.org

5, 7, 13, 19, 29, 41, 43, 47, 59, 61, 71, 73, 109, 127, 131, 137, 151, 163, 179, 223, 227, 233, 251, 263, 271, 277, 283, 331, 337, 347, 359, 367, 389, 421, 433, 461, 467, 499, 521, 523, 541, 547, 557, 563, 587, 593, 599, 601, 617, 641, 643, 653, 661, 673

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares mod 74", which is sequence A038913. - 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, A191042, A191043, A191047, A191049.

[p: p in PrimesUpTo(673) | KroneckerSymbol(p, 74) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,74]==1&]

select(p->kronecker(p, 74)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191046") 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

A191049 Primes p that have Kronecker symbol (p|82) = 1.

Original entry on oeis.org

3, 11, 13, 19, 23, 29, 31, 53, 67, 73, 101, 103, 109, 113, 127, 149, 157, 179, 181, 211, 223, 227, 229, 241, 271, 293, 317, 331, 337, 347, 353, 359, 367, 397, 401, 409, 421, 431, 433, 449, 487, 499, 509, 547, 557, 563, 569, 571, 587, 599, 607, 617, 631, 643

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares mod 82", which is sequence A038919. - 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, A191042, A191043, A191046, A191047.

[p: p in PrimesUpTo(643) | KroneckerSymbol(p, 82) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,82]==1&]

select(p->kronecker(p, 82)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191049") 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

A267455 Primes which are a square (mod 39).

Original entry on oeis.org

3, 13, 43, 61, 79, 103, 127, 139, 157, 181, 199, 211, 277, 283, 313, 337, 367, 373, 433, 439, 523, 547, 571, 601, 607, 673, 727, 751, 757, 823, 829, 859, 883, 907, 919, 937, 991, 997, 1039, 1063, 1069, 1093, 1117, 1153, 1171, 1213, 1231, 1249, 1291, 1297, 1303, 1327, 1381, 1429, 1447, 1453, 1459, 1483

Offset: 1

M. F. Hasler, Jan 15 2016

Motivated by the former (incorrect) definition of A191029.
Also, primes p which have Legendre symbols (p|3) = (p|13) = 1, together with 3 and 13.
Apparently this contains the 3 plus the elements of A139494. - R. J. Mathar, May 28 2025

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A038889, A045373, A056874, A106863, A106881, A191029.

Cf. A139494.

Join[{3, 13}, Select[Prime[Range[500]], JacobiSymbol[#, {3, 13}] == {1, 1} &]] (* Paolo Xausa, May 29 2025 *)

select(p->issquare(Mod(p,39))&&isprime(p),[1..1000])

cp's OEIS Frontend

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

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

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

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Magma

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A191043 Primes p that have Kronecker symbol (p|70) = 1.

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