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%I #34 Nov 19 2023 08:26:37
%S 4,5,9,13,17,57,105,137,3217,3229,4233,6097,8757,11457,12073,15425,
%T 40117,45357,334809,1509037
%N Numbers k such that 2^k - 13 is prime.
%C Except the first term 4, all terms are odd since for even k, 2^k - 13 is divisible by 3.
%H F. Firoozbakht and M. F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1.
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En-13">Search for 2^n-13</a>, PRP Top Records.
%e k = 5: 32 - 13 = 19 is prime.
%t Select[Range[4,20000],PrimeQ[2^#-13]&] (* _Vladimir Joseph Stephan Orlovsky_, Feb 27 2011 *)
%Y Cf. A096502.
%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), A059610 (d=9), A096817 (d=11), this sequence (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 _Labos Elemer_, Jul 13 2004
%E a(16) from _Max Alekseyev_, a(17)-a(18) from _Henri Lifchitz_, a(19) from Lelio R Paula, added by _Max Alekseyev_, Feb 09 2012
%E a(20) found by Stefano Morozzi, added by _Elmo R. Oliveira_, Nov 17 2023
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