A293048 Primes of the form 2^q * 3^r * 11^s + 1.

2, 3, 5, 7, 13, 17, 19, 23, 37, 67, 73, 89, 97, 109, 163, 193, 199, 257, 353, 397, 433, 487, 577, 727, 769, 1153, 1297, 1409, 1453, 1459, 1783, 2113, 2179, 2377, 2593, 2663, 2917, 3169, 3457, 3889, 4357, 5347, 6337, 7129, 8713, 10369, 11617, 12289, 15973, 17497, 18433, 19009, 19603

Offset: 1

Author

Muniru A Asiru, Sep 29 2017

Keywords

• nonn

Comments

Fermat prime exponents q occur in the case when q = 0, 1, 2, 4, 8, 16.

Examples

			2 = a(1) = 2^0 * 3^0 * 11^0 + 1.
13 = a(5) = 2^2 * 3^1 * 11^0 + 1 = 13.
list of (q, r, s): (0, 0, 0), (1, 0, 0), (2, 0, 0), (1, 1, 0), (2, 1, 0), (4, 0, 0), (1, 2, 0), (2, 0, 1), (2, 2, 0), (1, 1, 1), ...
		

Crossrefs

Cf. Sequences of primes of the form 2^q * 3^r * b^s + 1: A002200 (b = 5), A293008 (b = 7).

Programs

GAP

K:=10^5+1;; # to get all terms <= K.
A:=Filtered([1..K],IsPrime);;    I:=[3,11];;
B:=List(A,i->Elements(Factors(i-1)));;
C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;
A293048:=Concatenation([2],List(Set(Flat(List([1..Length(C)],i->List([1..Length(C[i])],j->Positions(B,C[i][j]))))),i->A[i]));

Mathematica

With[{n = 20000}, Union@ Select[Flatten@ Table[2^p1*3^p2*11^p5 + 1, {p1, 0, Log[2, n/(1)]}, {p2, 0, Log[3, n/(2^p1)]}, {p5, 0, Log[11, n/(2^p1*3^p2)]}], PrimeQ]] (* Michael De Vlieger, Sep 30 2017 *)