The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
KEYWORD
nonn
AUTHOR
Muniru A Asiru, Sep 26 2017
EXTENSIONS
More terms from Jinyuan Wang, Feb 23 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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