A059668 -id:A059668 - cp's OEIS frontend

A059264 Primes p such that x^12 = 2 has no solution mod p.

3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389

Offset: 1

Klaus Brockhaus, Jan 23 2001

Complement of A049544 relative to A000040.

Coincides for the first 119 terms with sequence of primes p such that x^36 = 2 has no solution mod p (first divergence is at 919, cf. A059668).

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A000040, A049544, A049568, A059668.

ok[p_] := Reduce[Mod[x^12 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]],ok] (* Vincenzo Librandi, Sep 14 2012 *)
Select[ Prime@ Range@ PrimePi@400, !MemberQ[ PowerMod[ Range@#, 12, #], Mod[2, #]] &] (* Robert G. Wilson v, Nov 05 2016 after Bruno Berselli in A059362 *)

A216484 Primes p such that x^36 = 2 has no solution mod p.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 29, 37, 41, 43, 53, 59, 61, 67, 73, 79, 83, 97, 101, 103, 107, 109, 131, 137, 139, 149, 151, 157, 163, 173, 179, 181, 193, 197, 199, 211, 227, 229, 241, 251, 269, 271, 277, 283, 293, 307, 313, 317, 331, 337, 347, 349, 367, 373, 379, 389

Offset: 1

Vincenzo Librandi, Sep 14 2012

Complement of A049568 relative to A000040.
Different from A059264: 919, 1423, 1999, ... (see A059668) are terms of this sequence, but not of A059264. [Joerg Arndt, Sep 14 2012]
Coincides for the first 416 terms with the sequence of primes p such that x^108 = 2 has no solution mod p (first divergence is at 3947). [Bruno Berselli, Sep 14 2012]

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Cf. A000040, A049568.

Cf. A059668 (primes p such that x^36 = 2 has no solution mod p, but x^12 = 2 has a solution mod p).

[p: p in PrimesUpTo(400) | forall{x: x in ResidueClassRing(p) | x^36 ne 2}];

ok[p_] := Reduce[Mod[x^36 - 2, p] == 0, x, Integers] == False; Select[Prime[Range[500]], ok]
Select[Prime[Range[PrimePi[400]]], ! MemberQ[PowerMod[Range[#], 36, #], Mod[2, #]] &] (* Bruno Berselli, Sep 14 2012 *)

A102645 Decimal expansion of (Pi*sqrt(163))^e.

Original entry on oeis.org

2, 2, 8, 0, 6, 9, 9, 9, 2, 3, 8, 5, 5, 6, 1, 3, 9, 2, 7, 1, 7, 0, 3, 8, 9, 8, 9, 3, 4, 4, 3, 3, 1, 1, 1, 5, 1, 1, 7, 5, 8, 8, 1, 6, 6, 2, 5, 0, 8, 3, 3, 0, 3, 9, 9, 3, 7, 4, 4, 7, 4, 0, 3, 5, 4, 9, 0, 6, 9, 5, 6, 0, 6, 3, 3, 0, 7, 3, 3, 9, 1, 2, 6, 7, 5, 7, 3, 1, 7, 2, 7, 4, 4, 7, 2, 9, 8, 4, 0, 6, 8, 8, 8, 8

Offset: 5

Gerald McGarvey, Feb 01 2005

The rounded value of this constant is 22807, a prime of the form p^2 + 6 where p is prime (cf. A079141), a balanced prime of order four (cf. A082079), a smallest prime larger than a square of an n-th prime, a largest prime == 7 mod 8 with class number 2n+1 (cf. A002147) and a prime p such that x^36 = 2 has no solution mod p, but x^12 = 2 has a solution mod p (cf. A059668).

			22806.99923855613927170389893443311151175881662508330399...

Cf. A060295.

RealDigits[(Pi*Sqrt[163])^E, 10, 111][[1]] (* Robert G. Wilson v, Feb 04 2005 *)

cp's OEIS Frontend

A059264 Primes p such that x^12 = 2 has no solution mod p.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A216484 Primes p such that x^36 = 2 has no solution mod p.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A102645 Decimal expansion of (Pi*sqrt(163))^e.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica