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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A002515, A101790, A101791, A101793.

Subsequence of A007522.

Subsequences: A101796, A101996.

Sequence in context: A118115 A020572 A021884 * A020346 A025964 A180361

Adjacent sequences: A101789 A101790 A101791 * A101793 A101794 A101795

Keyword

easy,nonn

Author

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

Status

approved