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A059608 Numbers k such that 2^k - 5 is prime.

%I A059608 #54 Apr 27 2025 05:12:50
%S A059608 3,4,6,8,10,12,18,20,26,32,36,56,66,118,130,150,166,206,226,550,706,
%T A059608 810,1136,1228,1818,2368,2400,3128,4532,5112,8492,16028,16386,17392,
%U A059608 18582,21986,24292,27618,30918,32762,48212,120440,183632,316140,364982,414032,533350,595122
%N A059608 Numbers k such that 2^k - 5 is prime.
%C A059608 Except 3, all terms are even since for odd k, 2^k - 5 is divisible by 3.
%H A059608 Keith Conrad, <a href="https://kconrad.math.uconn.edu/blurbs/ugradnumthy/squaresandinfmanyprimes.pdf">Square patterns and infinitude of primes</a>, University of Connecticut, 2019.
%H A059608 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.
%H A059608 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En-5">Search for 2^n-5</a>, PRP Top Records.
%e A059608 k = 10: 2^10 - 5 = 1019 is prime.
%e A059608 k = 20: 2^20 - 5 = 1048571 is prime.
%t A059608 Select[Range[2, 20000],PrimeQ[2^# - 5] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2011 *)
%o A059608 (PARI) is(n)=isprime(2^n-5) \\ _Charles R Greathouse IV_, Feb 17 2017
%Y A059608 Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), this sequence (d=5), A059609 (d=7), A059610 (d=9), A096817 (d=11), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), A356826 (d=29).
%K A059608 nonn
%O A059608 1,1
%A A059608 _Andrey V. Kulsha_, Jan 30 2001
%E A059608 a(32)-a(34) from _Labos Elemer_, Jul 09 2004
%E A059608 a(35)-a(40) from _Max Alekseyev_, a(41) from Paul Underwood, a(42)-a(46) from _Henri Lifchitz_, added by _Max Alekseyev_, Feb 09 2012
%E A059608 a(47)-a(48) from _Jon Grantham_, Jul 29 2023