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a(n) = least m > 1 such that m + 2^n is prime.
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%I #32 Nov 28 2015 19:33:37

%S 3,3,3,3,5,3,3,7,9,7,5,3,17,27,3,3,29,3,21,7,17,15,9,43,35,15,29,3,11,

%T 3,11,15,17,25,53,31,9,7,23,15,27,15,29,7,59,15,5,21,69,55,21,21,5,

%U 159,3,81,9,69,131,33,15,135,29,13,131,9,3,33,29,25,11,15,29,37,33

%N a(n) = least m > 1 such that m + 2^n is prime.

%C The definition is similar to Fortunate numbers (A005235) but uses 2^n instead of primorial A002110(n).

%C Terms a(n) are often but not always prime; sometimes they are prime powers or semiprimes or have a more general form.

%C An analog of Fortune's conjecture for this sequence would be "a(n) is either a prime power or a semiprime." But even this relaxed conjecture is disproved by, e.g., a(62)=135, a(93)=a(97)=105, a(99)=255.

%C By definition, a(n) >= A013597(n). The integers n such that a(n) > A013597(n) are those with A013597(n)=1, i.e., 1, 2, 4, 8, 16, and then? - _Michel Marcus_, Nov 06 2015

%H Charles R Greathouse IV, <a href="/A264050/b264050.txt">Table of n, a(n) for n = 1..2000</a>

%e a(56)=81 because m=81 is the least m > 1 such that m + 2^56 is prime.

%t Table[m = 2; While[! PrimeQ[m + 2^n], m++]; m, {n, 75}] (* _Michael De Vlieger_, Nov 06 2015 *)

%o (PARI) a(n)=my(m=2);while(!isprime(m+2^n),m++);m \\ _Anders Hellström_, Nov 02 2015

%o (PARI) a(n)=nextprime(2^n+2)-2^n \\ _Charles R Greathouse IV_, Nov 02 2015

%Y Cf. A005235, A013597, A092131, A263925.

%K nonn

%O 1,1

%A _Alexei Kourbatov_, Nov 02 2015

%E a(60) corrected by _Charles R Greathouse IV_, Nov 02 2015