%I #33 Nov 28 2023 18:34:19
%S 2,3,5,6,7,10,11,12,47,58,61,75,87,133,168,226,347,425,868,1977,2815,
%T 3378,4385,5286,7057,7200,8230,8340,13175,17226,18276,25237,33211,
%U 58463,59662,94555,120502,177473,197017,351097,375370,563190,673872,881002,1043375
%N Numbers k such that 4^k - 3 is prime.
%C The halved even terms of A050414. - _R. J. Mathar_, Feb 26 2008
%D 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]
%D 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]
%H Daniel Minoli, W. Nakamine, <a href="http://dx.doi.org/10.1109/ICASSP.1980.1170906">Mersenne Numbers Rooted On 3 For Number Theoretic Transforms</a>, 1980 IEEE International Conf. on Acoust., Speech and Signal Processing. [From Daniel Minoli (daniel.minoli(AT)ses.com), Aug 26 2009]
%e For k = 10, 4^10 - 3 = 1048573 is prime.
%t Select[Range[10000], PrimeQ[4^# - 3] &] (* _G. C. Greubel_, Jan 03 2016 *)
%o (PARI) is(n)=isprime(4^n-3) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y Cf. A050414, A217348 (similar sequence).
%K nonn
%O 1,1
%A _G. L. Honaker, Jr._, Jan 23 2001
%E 425 and 868 found by _Andrey V. Kulsha_, Feb 02 2001
%E More terms (not certified prime) from _Jason Earls_, Jan 04 2002
%E 9 more terms from _Ryan Propper_, Feb 27 2008
%E a(32)-a(41) derived from A050414 by _Robert Price_, Apr 26 2014
%E a(42)-a(45) derived from A050414 by _Elmo R. Oliveira_, Nov 28 2023