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Numbers k such that 5*2^k - 3 is prime.
1

%I #37 Mar 17 2024 13:57:40

%S 0,1,2,3,5,6,8,9,12,17,20,27,29,30,36,62,72,83,117,119,137,149,152,

%T 176,201,243,470,540,590,611,887,996,1118,1148,1269,1431,2099,2117,

%U 3822,5373,5640,6677,8352,19355,25937,27749,27948,34877,40536,46641,63891,66950,80451

%N Numbers k such that 5*2^k - 3 is prime.

%C a(49) > 37557. - _Jinyuan Wang_, Jan 21 2020

%C a(69) > 1000000. - _Jon Grantham_, Aug 04 2023

%H Jon Grantham, <a href="/A058588/b058588.txt">Table of n, a(n) for n = 1..68</a>

%H Jon Grantham and Andrew Granville, <a href="https://arxiv.org/abs/2307.07894">Fibonacci primes, primes of the form 2^n-k and beyond</a>, arXiv:2307.07894 [math.NT], 2023.

%t Do[ If[ PrimeQ[ 5*2^n - 3 ], Print[ n ] ], {n, 0, 10000} ]

%o (PARI) is(n)=ispseudoprime(5*2^n-3) \\ _Charles R Greathouse IV_, Jun 13 2017

%K nonn

%O 1,3

%A _Robert G. Wilson v_, Dec 26 2000

%E First term 0 inserted by _Georg Fischer_, Aug 01 2019

%E a(44)-a(48) from _Jinyuan Wang_, Jan 21 2020

%E a(49)-a(50) from _Michael S. Branicky_, May 20 2023

%E a(51) and beyond from _Jon Grantham_, Jul 30 2023