A101790 Numbers k such that 4*k-1, 8*k-1 and 16*k-1 are all primes.

3, 45, 90, 180, 255, 258, 363, 378, 453, 483, 615, 675, 705, 873, 885, 978, 1350, 1533, 1770, 1788, 2673, 2793, 2868, 3030, 3225, 3240, 4203, 4290, 4548, 4830, 4998, 5103, 5253, 5295, 5568, 5775, 5955, 6060, 6138, 6870, 7383, 7713, 8133, 8370, 8580, 9000

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

4*3 - 1 = 11, 8*3 - 1 = 23 and 16*3 - 1 = 47 are primes, so 3 is a term.

Mathematica

Select[Range[10^4], And @@ PrimeQ[2^Range[2, 4]*# - 1] &] (* Amiram Eldar, May 12 2024 *)

Prog

(Magma) [n: n in [0..10000] | IsPrime(4*n-1) and IsPrime(8*n-1) and IsPrime(16*n-1)]; // Vincenzo Librandi, Nov 17 2010
(PARI) is(k) = isprime(4*k-1) && isprime(8*k-1) && isprime(16*k-1); \\ Amiram Eldar, May 12 2024

Crossrefs

Cf. A002515, A101791, A101792, A101793.

Subsequence of A005099 and A005122.

Subsequences: A101794, A101994.

Sequence in context: A161589 A360966 A079038 * A124494 A075320 A071968

Adjacent sequences: A101787 A101788 A101789 * A101791 A101792 A101793

Keyword

easy,nonn

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Dec 16 2004

Status

approved