A101798 Primes of the form 32*k-1 such that 4*k-1, 8*k-1 and 16*k-1 are also primes.

1439, 2879, 21599, 28319, 96959, 137279, 219839, 429119, 462719, 507359, 571199, 597599, 659999, 700319, 811199, 858239, 861599, 903359, 976799, 982559, 1014719, 1017119, 1067999, 1115519, 1333919, 1342079, 1837919, 2029439, 2034239

Offset: 1

Author

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

Keywords

• easy
• nonn

Examples

			4*45-1 = 179, 8*45-1 = 359, 16*45-1 = 719 and 32*45-1 = 1439 are primes, so 1439 is a term.
		

Links

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

Crossrefs

Cf. A002515, A101794, A101795, A101796, A101797.

Subsequence of A127578.

Subsequence: A101998.

Programs

Mathematica

32 * Select[Range[10^5], And @@ PrimeQ[2^Range[2, 5]*# - 1] &] - 1 (* Amiram Eldar, May 13 2024 *)
Select[Prime[Range[200000]],Mod[#,32]==31&&AllTrue[{4,8,16} (#+1)/32-1,PrimeQ]&] (* Harvey P. Dale, Feb 20 2025 *)

PARI

is(k) = if(k % 32 == 31, my(m = k\32 + 1); isprime(4*m-1) && isprime(8*m-1) && isprime(16*m-1) && isprime(32*m-1), 0); \\ Amiram Eldar, May 13 2024

Formula

a(n) = 32*A101794(n) - 1 = 8*A101795(n) + 7 = 4*A101796(n) + 3 = 2*A101797(n) + 1. - Amiram Eldar, May 13 2024