Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #26 Dec 10 2023 09:17:13
%S 5,8,104,212,79316,102272,225536,340688
%N Numbers k such that 2^k - 29 is prime.
%C A particularly low-density pseudo-Mersenne sequence. I have verified that there are no additional terms for k < 5*10^4. For k = a(5), a(6), a(7), and a(8), 2^k - 29 is a probable prime (see link).
%C The terms a(5)-a(8) were discovered by Henri Lifchitz (see link). - _Elmo R. Oliveira_, Nov 29 2023
%C Empirically: except for 5, all terms are even. - _Elmo R. Oliveira_, Nov 29 2023
%H Henri Lifchitz and Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=2%5En-29">Search for 2^n-29</a>, PRP Top Records.
%e 5 is a term because 2^5 - 29 = 3 is prime.
%e 8 is a term because 2^8 - 29 = 227 is prime.
%o (PARI) for(n=2, 1000, if(isprime(2^n-29), print1(n, ", ")))
%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), A096818 (d=13), A059612 (d=15), A059611 (d=17), A096819 (d=19), A096820 (d=21), A057220 (d=23), this sequence (d=29).
%K nonn,more
%O 1,1
%A _Craig J. Beisel_, Aug 29 2022