A246956 Numbers a(n) = 2^(n-1) * f(n), where n >= 1 and f(n) is the smallest prime number larger than 2^n (A014210).

3, 10, 44, 136, 592, 2144, 8384, 32896, 133376, 527872, 2102272, 8394752, 33624064, 134438912, 536920064, 2147516416, 8591835136, 34360131584, 137444458496, 549759483904, 2199041081344, 8796124479488, 35184409837568, 140737849065472, 562950540623872, 2251800317001728, 9007201200898048, 36028797421617152, 144115191028645888, 576460753914036224, 2305843021024854016, 9223372069067030528

Offset: 1

Author

Hartmut F. W. Hoft, Sep 08 2014

Keywords

• nonn

Comments

The sequence is the "diagonal" - first element in each column - of the triangle of numbers associated with the symmetric representation of sigma(n) when it has two parts, each of width one (see A246955).

Examples

			a(4) = 8 * 17 = 136 since 17 is the first prime larger than 16.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A014210, A237270, A237271, A237593, A246955.

Programs

Mathematica

f[n_] := Module[{v = 2^n + 1}, While[!PrimeQ[v], v++]; v]
a[n_] := 2^(n - 1) f[n]
Map[a,Range[32]] (* data *)

PARI

a(n) = 2^(n-1) * nextprime(2^n+1); \\ Michel Marcus, Sep 23 2014