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

Author

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

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

Cf. A002515, A101791, A101792, A101793.

Subsequence of A005099 and A005122.

Subsequences: A101794, A101994.

Programs

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

Mathematica

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

PARI

is(k) = isprime(4*k-1) && isprime(8*k-1) && isprime(16*k-1); \\ Amiram Eldar, May 12 2024