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 A292890 Primes of the form 2^r * 17^s - 1. 1
 3, 7, 31, 67, 127, 271, 577, 1087, 2311, 8191, 78607, 131071, 524287, 1114111, 2367487, 2672671, 17825791, 42762751, 90870847, 606076927, 2147483647, 5151653887, 5815734271, 9697230847, 329705848831, 474351505987, 700624928767, 892896952447, 1168231104511, 2482491097087 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. For n > 1, all terms are congruent to 1 (mod 3). Also, these are prime numbers p for which (34^p)/(p+1) is an integer. LINKS Table of n, a(n) for n=1..30. EXAMPLE With n = 1, a(1) = 2^2 * 17^0 - 1 = 3. With n = 4, a(4) = 2^2 * 17^1 - 1 = 67. 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). PROG (GAP) K:=10^7+1;; # to get all terms <= K. A:=Filtered(Filtered([1..K], i->i mod 3=1), IsPrime);; I:=[17];; B:=List(A, i->Elements(Factors(i+1)));; C:=List([0..Length(I)], j->List(Combinations(I, j), i->Concatenation([2], i)));; 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])); (PARI) isok(p) = isprime(p) && (denominator((34^p)/(p+1)) == 1); \\ Michel Marcus, Sep 27 2017 CROSSREFS 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). Sequence in context: A365423 A080168 A183075 * A042131 A109140 A088193 Adjacent sequences: A292887 A292888 A292889 * A292891 A292892 A292893 KEYWORD nonn AUTHOR Muniru A Asiru, Sep 26 2017 EXTENSIONS More terms from Jinyuan Wang, Feb 23 2020 STATUS approved

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)