A059266 Numbers k such that 4^k - 3 is prime.

2, 3, 5, 6, 7, 10, 11, 12, 47, 58, 61, 75, 87, 133, 168, 226, 347, 425, 868, 1977, 2815, 3378, 4385, 5286, 7057, 7200, 8230, 8340, 13175, 17226, 18276, 25237, 33211, 58463, 59662, 94555, 120502, 177473, 197017, 351097, 375370, 563190, 673872, 881002, 1043375

Offset: 1

Author

G. L. Honaker, Jr., Jan 23 2001

Keywords

• nonn

Comments

The halved even terms of A050414. - R. J. Mathar, Feb 26 2008

Examples

			For k = 10, 4^10 - 3 = 1048573 is prime.
		

References

• Daniel Minoli, Voice over MPLS, McGraw-Hill, New York, NY, 2002, ISBN 0-07-140615-8 (p.114-134) [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]
• Daniel Minoli, New Results For Hyperperfect Numbers, Abstracts American Math. Soc., October 1980, Issue 6, Vol. 1, pp. 561. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]

Links

• Daniel Minoli, W. Nakamine, Mersenne Numbers Rooted On 3 For Number Theoretic Transforms, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]

Crossrefs

Cf. A050414, A217348 (similar sequence).

Programs

Mathematica

Select[Range[10000], PrimeQ[4^# - 3] &] (* G. C. Greubel, Jan 03 2016 *)

PARI

is(n)=isprime(4^n-3) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

425 and 868 found by Andrey V. Kulsha, Feb 02 2001

More terms (not certified prime) from Jason Earls, Jan 04 2002

9 more terms from Ryan Propper, Feb 27 2008

a(32)-a(41) derived from A050414 by Robert Price, Apr 26 2014

a(42)-a(45) derived from A050414 by Elmo R. Oliveira, Nov 28 2023