A074717 Least k such that floor(2^n/k) is prime.

1, 2, 3, 3, 6, 9, 11, 11, 7, 9, 5, 10, 19, 11, 5, 10, 9, 11, 22, 35, 39, 9, 5, 10, 20, 27, 11, 19, 9, 18, 36, 25, 29, 27, 5, 10, 20, 40, 61, 13, 21, 42, 29, 27, 39, 9, 17, 29, 58, 49, 27, 25, 50, 11, 22, 44, 39, 11, 22, 44, 29, 58, 116, 53, 19, 38, 76, 152, 237, 139, 5, 10, 20

Offset: 1

Author

Benoit Cloitre, Sep 04 2002

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013597, A013603, A035050, A085427.

Programs

Mathematica

a[n_] := Module[{k = 1}, While[! PrimeQ @ Floor[2^n/k], k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 31 2020 *)

PARI

a(n)=if(n<0,0,k=1; while(isprime(floor(2^n/k)) == 0,k++); k)

Formula

There is probably a constant c such that Sum_{i=1..n} a(i) is asymptotic to c*n^2 (0 < c < 1/2).