A068231 Primes congruent to 11 mod 12.

11, 23, 47, 59, 71, 83, 107, 131, 167, 179, 191, 227, 239, 251, 263, 311, 347, 359, 383, 419, 431, 443, 467, 479, 491, 503, 563, 587, 599, 647, 659, 683, 719, 743, 827, 839, 863, 887, 911, 947, 971, 983, 1019, 1031, 1091, 1103, 1151, 1163, 1187, 1223

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

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

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

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

Links

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

Crossrefs

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

Programs

MATLAB

%4n-1 and 6n-1 primes
n = 1:10000;
n2 = 4*n-1;
n3 = 3*n-1;
p = primes(max(n2));
Res = intersect(n2,n3);
Res2 = intersect(Res,p);
% Jesse H. Crotts, Sep 25 2016

Magma

[p: p in PrimesUpTo(1500) | p mod 12 eq 11 ]; // Vincenzo Librandi, Aug 14 2012

Mathematica

Select[Prime/@Range[250], Mod[ #, 12]==11&]
Select[Range[11,1500,12],PrimeQ] (* Harvey P. Dale, Sep 15 2023 *)

PARI

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

Extensions

Edited by Dean Hickerson, Feb 27 2002