A293048 - OEIS

%I #7 Sep 30 2017 23:48:18

%S 2,3,5,7,13,17,19,23,37,67,73,89,97,109,163,193,199,257,353,397,433,

%T 487,577,727,769,1153,1297,1409,1453,1459,1783,2113,2179,2377,2593,

%U 2663,2917,3169,3457,3889,4357,5347,6337,7129,8713,10369,11617,12289,15973,17497,18433,19009,19603

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

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

%e 2 = a(1) = 2^0 * 3^0 * 11^0 + 1.

%e 13 = a(5) = 2^2 * 3^1 * 11^0 + 1 = 13.

%e 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), ...

%t 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 *)

%o (GAP)

%o K:=10^5+1;; # to get all terms <= K.

%o A:=Filtered([1..K],IsPrime);;    I:=[3,11];;

%o B:=List(A,i->Elements(Factors(i-1)));;

%o C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;

%o 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]));

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

%K nonn

%O 1,1

%A _Muniru A Asiru_, Sep 29 2017