login
Primes congruent to 11 mod 12.
38

%I #48 Sep 15 2023 16:34:19

%S 11,23,47,59,71,83,107,131,167,179,191,227,239,251,263,311,347,359,

%T 383,419,431,443,467,479,491,503,563,587,599,647,659,683,719,743,827,

%U 839,863,887,911,947,971,983,1019,1031,1091,1103,1151,1163,1187,1223

%N Primes congruent to 11 mod 12.

%C Intersection of A002145 (primes of form 4n+3) and A003627 (primes of form 3n-1). So these are both Gaussian primes with no imaginary part and Eisenstein primes with no imaginary part. - _Alonso del Arte_, Mar 29 2007

%C Is this the same sequence as A141187 (apart from the initial 3)?

%C If p is prime of the form 2*a(n)^k + 1, then p divides a cyclotomic number Phi(a(n)^k, 2). - _Arkadiusz Wesolowski_, Jun 14 2013

%C Also a(n) = primes p dividing A014138((p-3)/2), where A014138(n) = Partial sums of (Catalan numbers starting 1,2,5,...), cf. A000108. - _Alexander Adamchuk_, Dec 27 2013

%H Vincenzo Librandi, <a href="/A068231/b068231.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Prime/@Range[250], Mod[ #, 12]==11&]

%t Select[Range[11,1500,12],PrimeQ] (* _Harvey P. Dale_, Sep 15 2023 *)

%o (PARI) for(i=1,250, if(prime(i)%12==11, print(prime(i))))

%o (Magma) [p: p in PrimesUpTo(1500) | p mod 12 eq 11 ]; // _Vincenzo Librandi_, Aug 14 2012

%o (MATLAB)

%o %4n-1 and 6n-1 primes

%o n = 1:10000;

%o n2 = 4*n-1;

%o n3 = 3*n-1;

%o p = primes(max(n2));

%o Res = intersect(n2,n3);

%o Res2 = intersect(Res,p);

%o % _Jesse H. Crotts_, Sep 25 2016

%Y Cf. A068227, A068228, A068229, A040117, A068232, A068233, A068234, A068235, A000040, A014138, A000108.

%K easy,nonn

%O 1,1

%A Ferenc Adorjan (fadorjan(AT)freemail.hu), Feb 22 2002

%E Edited by _Dean Hickerson_, Feb 27 2002