A045473 - OEIS

%I #50 Sep 08 2022 08:44:56

%S 13,41,83,97,139,167,181,223,251,293,307,349,419,433,461,503,587,601,

%T 643,727,769,797,811,839,853,881,937,1021,1049,1063,1091,1217,1231,

%U 1259,1301,1399,1427,1483,1511,1553,1567,1609,1637,1693,1721,1777,1847,1861

%N Primes congruent to 6 mod 7.

%C Conjecture: Primes p such that ((x+1)^7-1)/x has 3 irreducible factors of degree 2 over GF(p). - _Federico Provvedi_, Mar 31 2018

%C Also primes of the form 14*k + 13. - _David A. Corneth_, Apr 02 2018

%H Vincenzo Librandi, <a href="/A045473/b045473.txt">Table of n, a(n) for n = 1..1000</a>

%p select(n->isprime(n) and modp(n,7)=6,[$1..1900]); # _Muniru A Asiru_, Mar 31 2018

%t Select[Range[6,1600,7],PrimeQ] (* _Bruno Berselli_, Aug 17 2012 *)

%o (Magma) [ p: p in PrimesUpTo(11000) | p mod 7 eq 6 ]; // _Vincenzo Librandi_, Aug 13 2012

%o (PARI) is(n)=isprime(n) && n%7==6 \\ _Charles R Greathouse IV_, Jul 01 2016

%o (GAP) Filtered([1..1900],n->IsPrime(n) and n mod 7 = 6); # _Muniru A Asiru_, Mar 31 2018

%Y Cf. A042988 (complement).

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_