A191036 -id:A191036 - cp's OEIS frontend

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

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

A191051 Primes p that have Kronecker symbol (p|86) = 1.

Original entry on oeis.org

3, 5, 17, 19, 23, 29, 31, 37, 41, 47, 61, 79, 97, 103, 127, 131, 149, 157, 163, 167, 179, 193, 211, 227, 239, 271, 277, 281, 311, 331, 337, 347, 349, 353, 359, 367, 373, 389, 401, 419, 421, 431, 439, 467, 479, 487, 491, 499, 523, 569, 571, 587, 599, 617, 653

Offset: 1

T. D. Noe, May 25 2011

Originally incorrectly named "primes which are squares mod 86", which is sequence A106891. - 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, A191049.

[p: p in PrimesUpTo(653) | KroneckerSymbol(p, 86) eq 1]; // Vincenzo Librandi, Sep 11 2012

Select[Prime[Range[200]], JacobiSymbol[#,86]==1&]

select(p->kronecker(p, 86)==1&&isprime(p), [1..1000]) \\ This is to provide a generic characteristic function ("is_A191051") as 1st arg of select(), there are other ways to produce the sequence more efficiently. - M. F. Hasler, Jan 15 2016

Definition corrected by M. F. Hasler, Jan 15 2016

A191074 Primes p that have Kronecker symbol (p|55) = -1.

Original entry on oeis.org

3, 19, 23, 29, 37, 41, 47, 53, 61, 67, 79, 97, 101, 103, 109, 113, 131, 137, 139, 149, 151, 157, 163, 211, 223, 239, 241, 257, 271, 281, 313, 317, 349, 353, 359, 367, 383, 397, 409, 431, 433, 439, 443, 461, 463, 467, 479, 487, 491, 541, 569, 571, 577, 587

Offset: 1

T. D. Noe, May 25 2011

Originally erroneously named "Primes that are not squares mod 55", which contains this as a subsequence. - M. F. Hasler, Jan 18 2016

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

Cf. A191036.

[p: p in PrimesUpTo(587) | JacobiSymbol(p, 55) eq -1]; // Vincenzo Librandi, Sep 11 2012

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

Definition corrected, following a suggestion from David Broadhurst, by M. F. Hasler, Jan 18 2016

A267478 Primes which are squares (mod 55).

Original entry on oeis.org

5, 11, 31, 59, 71, 89, 179, 181, 191, 199, 229, 251, 269, 311, 331, 379, 389, 401, 419, 421, 449, 499, 509, 521, 599, 619, 631, 641, 661, 691, 709, 719, 751, 829, 839, 859, 881, 911, 929, 971, 991, 1021, 1039, 1049, 1061, 1109, 1171, 1181, 1259, 1279, 1291, 1301, 1321, 1409, 1439, 1489, 1499

Offset: 1

M. F. Hasler, Jan 15 2016

nonn

5, 11 and all primes congruent to 1, 4, 9, 14, 16, 26, 31, 34, 36, or 49 (mod 55). - Robert Israel, Jan 15 2016

Cf. A106904 and adjacent sequences.

Cf. A191036.

S55:= {seq(x^2 mod 55, x=0..27)}:
select(t -> member(t mod 55, S55), [seq(ithprime(i),i=1..1000)]); # Robert Israel, Jan 15 2016

Join[{5,11},Select[Prime[Range[250]],MemberQ[{1,4,9,14,16,26,31,34,36,49},Mod[#,55]]&]] (* Harvey P. Dale, Jan 17 2022 *)

select(p->issquare(Mod(p,55))&&isprime(p),[1..1500]) \\ It would be more efficient to select only among primes, replacing [1..1500] by primes([1,1500]), in which case the isprime() condition can be omitted from the selection function. But we wanted to provide a universally valid characteristic function in the 1st argument of select(). - M. F. Hasler, Jan 15 2016

cp's OEIS Frontend

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

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

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

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