A059223 -id:A059223 - cp's OEIS frontend

A142112 Primes congruent to 2 mod 37.

2, 113, 409, 557, 631, 853, 1223, 1297, 1667, 1741, 1889, 2111, 2333, 2777, 2851, 2999, 3221, 3517, 3739, 5441, 5737, 6329, 6551, 7069, 7883, 8179, 8623, 9067, 9437, 9511, 9733, 10103, 10177, 10399, 11213, 11287, 11657, 11731, 11953, 12101, 12323, 12619

Offset: 1

N. J. A. Sloane, Jul 11 2008

2 and primes congruent to 39 mod 74. - Chai Wah Wu, Apr 29 2025

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

Cf. A000040, A059223.

[p: p in PrimesUpTo(15000) | p mod 37 eq 2 ]; // Vincenzo Librandi, Aug 19 2012

Select[Range[2,20000,37],PrimeQ] (* Vladimir Joseph Stephan Orlovsky, May 07 2011 *)
Select[Prime[Range[5000]],MemberQ[{2},Mod[#,37]]&] (* Vincenzo Librandi, Aug 19 2012 *)

is(n)=isprime(n) && n%37==2 \\ Charles R Greathouse IV, Jul 02 2016

a(n) ~ 36n log n. - Charles R Greathouse IV, Jul 02 2016

A049569 Primes p such that x^37 = 2 has a solution mod p.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281

Offset: 1

N. J. A. Sloane

Complement of A059223 relative to A000040. - Vincenzo Librandi, Sep 14 2012

R. J. Mathar, Table of n, a(n) for n = 1..1000
Index entries for related sequences

Cf. A000040, A059223.

[p: p in PrimesUpTo(300) | exists(t){x : x in ResidueClassRing(p) | x^37 eq 2}]; // Vincenzo Librandi, Sep 14 2012

ok[p_]:= Reduce[Mod[x^37 - 2, p] == 0, x, Integers] =!= False; Select[Prime[Range[100]], ok] (* Vincenzo Librandi, Sep 14 2012 *)

N=10^4;  default(primelimit,N);
ok(p, r, k)={ return ( (p==r) || (Mod(r,p)^((p-1)/gcd(k,p-1))==1) ); }
forprime(p=2,N, if (ok(p,2,37),print1(p,", ")));
/* Joerg Arndt, Sep 21 2012 */

A216970 Primes congruent to 1 mod 37.

Original entry on oeis.org

149, 223, 593, 1259, 1481, 1777, 1999, 2221, 2591, 2887, 3109, 3257, 3331, 3701, 3923, 4219, 4441, 4663, 5107, 5477, 6143, 6217, 6661, 6883, 7253, 7549, 7919, 7993, 8363, 8807, 9029, 9103, 9473, 9547, 9769, 10139, 10657, 11027, 11471, 12211, 12433, 13099

Offset: 1

Bruno Berselli, Sep 21 2012

Coincides for the first 38 terms with A059223 (primes p such that x^37 = 2 has no solution mod p), the first divergence is at the term 11471.

Bruno Berselli, Table of n, a(n) for n = 1..1000

Cf. A000040, A059223, A100203, A142112-A142145.

[p: p in PrimesUpTo(14000) | IsOne(p mod 37)];

Select[Prime[Range[1700]], Mod[#, 37] == 1 &]
Select[Range[1, 14000, 37], PrimeQ]

select(p->p%37==1,primes(10^4)) /* Joerg Arndt, Sep 21 2012 */

cp's OEIS Frontend

A142112 Primes congruent to 2 mod 37.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A049569 Primes p such that x^37 = 2 has a solution mod p.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A216970 Primes congruent to 1 mod 37.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI