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Numbers a(n) = 2^(n-1) * f(n), where n >= 1 and f(n) is the smallest prime number larger than 2^n (A014210).
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%I #16 Nov 21 2014 16:30:55

%S 3,10,44,136,592,2144,8384,32896,133376,527872,2102272,8394752,

%T 33624064,134438912,536920064,2147516416,8591835136,34360131584,

%U 137444458496,549759483904,2199041081344,8796124479488,35184409837568,140737849065472,562950540623872,2251800317001728,9007201200898048,36028797421617152,144115191028645888,576460753914036224,2305843021024854016,9223372069067030528

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

%C 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).

%H Jens Kruse Andersen, <a href="/A246956/b246956.txt">Table of n, a(n) for n = 1..1000</a>

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

%t f[n_] := Module[{v = 2^n + 1}, While[!PrimeQ[v], v++]; v]

%t a[n_] := 2^(n - 1) f[n]

%t Map[a,Range[32]] (* data *)

%o (PARI) a(n) = 2^(n-1) * nextprime(2^n+1); \\ _Michel Marcus_, Sep 23 2014

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

%K nonn

%O 1,1

%A _Hartmut F. W. Hoft_, Sep 08 2014