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A268607 a(n) is the least m > 1 such that 2^n - m is prime.

%I A268607 #15 Mar 10 2025 11:02:10
%S A268607 2,3,3,3,3,15,5,3,3,9,3,13,3,19,15,9,5,19,3,9,3,15,3,39,5,39,57,3,35,
%T A268607 19,5,9,41,31,5,25,45,7,87,21,11,57,17,55,21,115,59,81,27,129,47,111,
%U A268607 33,55,5,13,27,55,93,31,57,25,59,49,5,19,23,19,35,231,93
%N A268607 a(n) is the least m > 1 such that 2^n - m is prime.
%C A268607 a(1) is not defined (there are no primes less than 2).
%C A268607 The definition is similar to Lesser Fortunate numbers (A055211) but uses 2^n instead of primorials A002110(n).
%H A268607 Paolo Xausa, <a href="/A268607/b268607.txt">Table of n, a(n) for n = 2..1000</a>
%F A268607 a(n) = A013603(n), if A013603(n) > 1. - _Jason Yuen_, Mar 10 2025
%e A268607 a(7)=15 because m=15 is the least m > 1 such that 2^7 - m is prime.
%t A268607 Map[# - NextPrime[#-1, -1] &, 2^Range[2, 100]] (* _Paolo Xausa_, Mar 10 2025 *)
%o A268607 (PARI) a(n)=2^n-precprime(2^n-2)
%Y A268607 Cf. A005235, A013603, A055211, A264050, A263925, A268608.
%K A268607 nonn
%O A268607 2,1
%A A268607 _Alexei Kourbatov_, Feb 08 2016