A264050 a(n) = least m > 1 such that m + 2^n is prime.

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, 3, 11, 15, 17, 25, 53, 31, 9, 7, 23, 15, 27, 15, 29, 7, 59, 15, 5, 21, 69, 55, 21, 21, 5, 159, 3, 81, 9, 69, 131, 33, 15, 135, 29, 13, 131, 9, 3, 33, 29, 25, 11, 15, 29, 37, 33

Offset: 1

Author

Alexei Kourbatov, Nov 02 2015

Keywords

• nonn

Comments

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

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

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.

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

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A005235, A013597, A092131, A263925.

Programs

Mathematica

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

PARI

a(n)=my(m=2);while(!isprime(m+2^n),m++);m \\ Anders Hellström, Nov 02 2015

PARI

a(n)=nextprime(2^n+2)-2^n \\ Charles R Greathouse IV, Nov 02 2015

Extensions

a(60) corrected by Charles R Greathouse IV, Nov 02 2015