A253398 Smallest odd k > 1 such that k*2^prime(n) + 1 is prime.

3, 5, 3, 5, 9, 5, 9, 11, 45, 23, 35, 15, 3, 9, 27, 51, 27, 53, 9, 39, 23, 249, 51, 51, 131, 221, 29, 105, 321, 179, 5, 221, 111, 411, 191, 65, 83, 75, 95, 101, 147, 83, 149, 111, 203, 131, 9, 245, 281, 15, 83, 65, 299

Offset: 1

Author

Pierre CAMI, Dec 31 2014

Keywords

• nonn

Comments

For n < 1275, the ratio a(n)/prime(n) is always < 6 and on average ~0.7.

From Robert G. Wilson v, Jan 27 2015: (Start)

Records: 3, 5, 9, 11, 45, 51, 53, 249, 321, 411, 611, 1383, 1875, 2423, 4239, 4623, 6549, 7095, 8091, 9003, 10065, 10719, 18005, 18545, 19251, 21111, 25409, 39741, 49709, 54455, ..., .

a(n)=3 for n = 1, 3, 13, 71, ...;

a(n)=5 for n = 2, 4, 6, 31, 466, ...;

a(n)=9 for n = 5, 7, 14, 19, 47, 342, 1167, ...;

a(n)=11 for n = 8, ...; etc.

(End)

Examples

			3*2^2 + 1 = 13 (prime), so a(1)=3.
3*2^3 + 1 = 25 (composite), 5*2^3 + 1 = 41 (prime), so a(2)=5.
3*2^5 + 1 = 97 (prime), so a(3)=3.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1500 (first 1275 terms from Pierre CAMI)

Crossrefs

Cf. A247479, A253027.

Programs

Mathematica

f[n_] := Block[{k = 3, p = 2^Prime@ n}, While[ !PrimeQ[ k*p + 1], k += 2]; k]; Array[f, 53] (* Robert G. Wilson v, Jan 25 2015 *)

PARI

a(n)=k=1;while(!isprime((2*k+1)*2^prime(n)+1),k++);2*k+1
vector(100,n,a(n)) \\ Derek Orr, Dec 31 2014

Formula

a(n) = A247479(p_n). - Robert G. Wilson v, Jan 27 2015