A059230 -id:A059230 - cp's OEIS frontend

A212378 Primes congruent to 1 mod 61.

367, 733, 977, 1709, 1831, 2441, 3539, 4027, 4271, 4637, 4759, 5003, 5857, 6101, 6833, 7321, 7687, 8053, 8297, 8419, 8663, 9029, 9151, 9883, 10859, 12323, 12689, 13177, 13421, 14153, 14519, 15373, 15739, 16349, 17203, 17569, 18301, 18911, 21107, 21839, 21961

Offset: 1

Bruno Berselli, Sep 20 2012

Coincides for the first 58 terms with A059230, that is the sequence of primes p such that x^61 = 2 has no solution mod p (first divergence is at 34039).

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

Cf. A000040, A059230, A142800-A142858.

[p: p in PrimesUpTo(22000) | IsOne(p mod 61)];

Select[Prime[Range[2500]], Mod[#, 61] == 1 &]
Select[Range[1, 22000, 61], PrimeQ]

is(n)=isprime(n) && n%61==1 \\ Charles R Greathouse IV, Jul 03 2016

a(n) ~ 60n log n. - Charles R Greathouse IV, Jul 03 2016

A216884 Primes p such that x^61 = 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, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271

Offset: 1

Vincenzo Librandi, Sep 19 2012

Complement of A059230 relative to A000040.

Naturally this sequence is not the same as A000040. First disagreement at index 73: a(73)=373, A000040(73)=367. [Bruno Berselli, Sep 20 2012]

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

[p: p in PrimesUpTo(500) | exists(t){x: x in ResidueClassRing(p) | x^61 eq 2}];

ok[p_] := Reduce[Mod[x^61 - 2, p] == 0, x, Integers] == True; Select[Prime[Range[150]], ok]

cp's OEIS Frontend

A212378 Primes congruent to 1 mod 61.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula