A101795 Primes of the form 4*k-1 such that 8*k-1, 16*k-1 and 32*k-1 are also primes.

179, 359, 2699, 3539, 12119, 17159, 27479, 53639, 57839, 63419, 71399, 74699, 82499, 87539, 101399, 107279, 107699, 112919, 122099, 122819, 126839, 127139, 133499, 139439, 166739, 167759, 229739, 253679, 254279, 287219, 296099

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 179 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A002515, A101794, A101796, A101797, A101798.

Subsequence of A002145 and A101791.

Subsequence: A101995.

Programs

Mathematica

Select[Table[4n-1,{n,75000}],AllTrue[(#+1)*{1,2,4,8}-1,PrimeQ]&] (* Harvey P. Dale, Apr 23 2019 *)

PARI

is(k) = if(k % 4 == 3, my(m = k\4 + 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) = 4*A101794(n) - 1. - Amiram Eldar, May 13 2024