A101792 Primes of the form 8*k-1 such that 4*k-1 and 16*k-1 are also primes.

23, 359, 719, 1439, 2039, 2063, 2903, 3023, 3623, 3863, 4919, 5399, 5639, 6983, 7079, 7823, 10799, 12263, 14159, 14303, 21383, 22343, 22943, 24239, 25799, 25919, 33623, 34319, 36383, 38639, 39983, 40823, 42023, 42359, 44543, 46199, 47639, 48479, 49103, 54959

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 23 is a term.
		

Links

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

Crossrefs

Cf. A002515, A101790, A101791, A101793.

Subsequence of A007522.

Subsequences: A101796, A101996.

Programs

Mathematica

8 * Select[Range[10^4], And @@ PrimeQ[2^Range[2, 4]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)

PARI

for(k=1,7000,if(isprime(8*k-1)&&isprime(4*k-1)&&isprime(16*k-1),print1(8*k-1,", "))) \\ Hugo Pfoertner, Sep 07 2021

Formula

a(n) = 8*A101790(n) - 1 = 2*A101791(n) + 1. - Amiram Eldar, May 13 2024