A045463 Primes congruent to {0, 1, 6} mod 7.

7, 13, 29, 41, 43, 71, 83, 97, 113, 127, 139, 167, 181, 197, 211, 223, 239, 251, 281, 293, 307, 337, 349, 379, 419, 421, 433, 449, 461, 463, 491, 503, 547, 587, 601, 617, 631, 643, 659, 673, 701, 727, 743, 757

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The prime factors of x^3 - x^2 - 2x + 1 come exclusively from this sequence. - Charles R Greathouse IV, Mar 18 2022

Links

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

Crossrefs

Cf. A000040.

Programs

Magma

[ p: p in PrimesUpTo(900) | p mod 7 in {0, 1, 6} ]; // Vincenzo Librandi, Aug 13 2012

Mathematica

Select[Prime[Range[200]],MemberQ[{0,1,6},Mod[#,7]]&] (* Vincenzo Librandi, Aug 13 2012 *)

PARI

select(p->abs(centerlift(Mod(p,7)))<2, primes(100)) \\ Charles R Greathouse IV, Mar 17 2022

Formula

A045472 UNION {7}. - R. J. Mathar, Oct 18 2008

a(n) ~ 3n log n. - Charles R Greathouse IV, Mar 17 2022