A217348 Numbers k such that 4^k - 5 is prime.

2, 3, 4, 5, 6, 9, 10, 13, 16, 18, 28, 33, 59, 65, 75, 83, 103, 113, 275, 353, 405, 568, 614, 909, 1184, 1200, 1564, 2266, 2556, 4246, 8014, 8193, 8696, 9291, 10993, 12146, 13809, 15459, 16381, 24106, 60220, 91816, 158070, 182491, 207016, 266675, 297561

Offset: 1

Author

Vincenzo Librandi, Oct 01 2012

Keywords

• nonn
• more

Examples

			28 is a term because 4^28 - 5 = 72057594037927931 is prime.
		

Crossrefs

Cf. A059266, A059608, A059614.

Programs

Mathematica

Select[Range[10000], PrimeQ[4^# - 5] &]

PARI

/* Up to 620 the code produces in few seconds the first terms: */
allocatemem(10000000); for(n=2, 620, if(isprime(4^n-5), print1(n", ")));

Formula

a(n) = A059608(n+1)/2. - Daniel Starodubtsev, Mar 20 2020

Extensions

a(31)-a(34) from Bruno Berselli, Oct 02 2012

a(35)-a(45) from Daniel Starodubtsev, Mar 20 2020

a(46)-a(47) derived from A059608 by Elmo R. Oliveira, Nov 28 2023