Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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