cp's OEIS Frontend

A292890 Primes of the form 2^r * 17^s - 1.

%I A292890 #10 Feb 23 2020 20:57:50
%S A292890 3,7,31,67,127,271,577,1087,2311,8191,78607,131071,524287,1114111,
%T A292890 2367487,2672671,17825791,42762751,90870847,606076927,2147483647,
%U A292890 5151653887,5815734271,9697230847,329705848831,474351505987,700624928767,892896952447,1168231104511,2482491097087
%N A292890 Primes of the form 2^r * 17^s - 1.
%C A292890 Primes of the forms 2^r * b^s - 1 where b = 1, 5, 7, 11, 13 are A000668 (Mersenne prime exponents), A077313, A077314, A077315 and A173062. When b = 3 we get A005105 with initial term 2.
%C A292890 For n > 1, all terms are congruent to 1 (mod 3).
%C A292890 Also, these are prime numbers p for which (34^p)/(p+1) is an integer.
%e A292890 With n = 1, a(1) = 2^2 * 17^0 - 1 = 3.
%e A292890 With n = 4, a(4) = 2^2 * 17^1 - 1 = 67.
%e A292890 list of (r, s): (2, 0), (3, 0), (5, 0), (2, 1), (3, 1), (7, 0), (4, 1), (1, 2), (6, 1), (3, 2), (13, 0), (4, 3), (17, 0), (19, 0), (16, 1), (13, 2), (5, 4), (20, 1), (9, 4), (6, 5).
%o A292890 (GAP)
%o A292890 K:=10^7+1;; # to get all terms <= K.
%o A292890 A:=Filtered(Filtered([1..K], i->i mod 3=1),IsPrime);;    I:=[17];;
%o A292890 B:=List(A,i->Elements(Factors(i+1)));;
%o A292890 C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;
%o A292890 A292890:=Concatenation([3],List(Set(Flat(List([1..Length(C)],i->List([1..Length(C[i])],j->Positions(B,C[i][j]))))),i->A[i]));
%o A292890 (PARI) isok(p) = isprime(p) && (denominator((34^p)/(p+1)) == 1); \\ _Michel Marcus_, Sep 27 2017
%Y A292890 Cf. Sequences of primes of the forms 2^n * q^s - 1: A000668 (q = 1), A005105 (q = 3), A077313 (q = 5), A077314 (q = 7), A077315 (q = 11), A173062 (q = 13).
%K A292890 nonn
%O A292890 1,1
%A A292890 _Muniru A Asiru_, Sep 26 2017
%E A292890 More terms from _Jinyuan Wang_, Feb 23 2020