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

1,1

Comments

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

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

Table of n, a(n) for n=1..45.

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]

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A050414, A217348 (similar sequence).

Sequence in context: A136149 A101882 A318239 * A336222 A252895 A366242

Adjacent sequences: A059263 A059264 A059265 * A059267 A059268 A059269

Keyword

nonn

Author

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

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

Status

approved