%I #44 Nov 25 2023 08:42:39

%S 4,5,9,11,17,21,33,125,141,243,251,285,321,537,563,699,729,2841,3365,

%T 8451,8577,9699,9725,21011,22689,33921,51761,655845,676761,3480081

%N Numbers k such that 2^k - 9 is prime.

%C Except the first term 4, all terms are odd since 2^(2*m) - 9 = (2^m - 3)*(2^m + 3) is not prime for m > 2.

%H 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 Henri Lifchitz and Renaud Lifchitz (Editors), <a href="https://www.primenumbers.net/prptop/searchform.php?form=2%5En-9">Search for 2^n-9</a>, PRP Top Records.

%e 243 is in the sequence because 2^243 - 9 is prime.

%t Select[Range[3,20000],PrimeQ[2^#-9]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2011 *)

%o (PARI) is(n)=isprime(2^n-9) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. Sequences of numbers k such that 2^k - d is prime: A000043 (d=1), A050414 (d=3), A059608 (d=5), A059609 (d=7), this sequence (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 nonn,more

%O 1,1

%A _Andrey V. Kulsha_, Feb 02 2001

%E a(24)-a(25) from Max Alekseyev, a(26)-a(27) from Paul Underwood, added by _Max Alekseyev_, Feb 09 2012

%E a(28)-a(29) from _Robert Price_, Jan 25 2017

%E a(30) found by Stefano Morozzi, added by _Elmo R. Oliveira_, Nov 17 2023