cp's OEIS Frontend

A293008 Primes of the form 2^q * 3^r * 7^s + 1.

%I A293008 #8 Sep 30 2017 23:48:11
%S A293008 2,3,5,7,13,17,19,29,37,43,73,97,109,113,127,163,193,197,257,337,379,
%T A293008 433,449,487,577,673,757,769,883,1009,1153,1297,1373,1459,2017,2269,
%U A293008 2593,2647,2689,2917,3137,3457,3529,3889,7057,8233,10369,10753,12097,12289,14407,15877,17497,18433
%N A293008 Primes of the form 2^q * 3^r * 7^s + 1.
%C A293008 Fermat prime exponents q occur in the case when q = 0, 1, 2, 4, 8, 16.
%e A293008 With n = 1,  a(1) = 2^0 * 3^0 * 7^0 + 1 = 2.
%e A293008 With n = 5,  a(5) = 2^2 * 3^1 * 7^0 + 1 = 13.
%e A293008 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 A293008 With[{n = 19000}, Union@ Select[Flatten@ Table[2^p1*3^p2*7^p4 + 1, {p1, 0, Log[2, n/(1)]}, {p2, 0, Log[3, n/(2^p1)]}, {p4, 0, Log[7, n/(2^p1*3^p2)]}], PrimeQ]] (* _Michael De Vlieger_, Sep 30 2017 *)
%o A293008 (GAP)
%o A293008 K:=10^7+1;; # to get all terms <= K.
%o A293008 A:=Filtered([1..K],IsPrime);;    I:=[3,7];;
%o A293008 B:=List(A,i->Elements(Factors(i-1)));;
%o A293008 C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;
%o A293008 A293008:=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 A293008 Cf. A002200 (Primes of the form 2^q * 3^r * 5^s + 1).
%K A293008 nonn
%O A293008 1,1
%A A293008 _Muniru A Asiru_, Sep 28 2017