A301797 a(n) = (4^prime(n) - 1)/3.
5, 21, 341, 5461, 1398101, 22369621, 5726623061, 91625968981, 23456248059221, 96076792050570581, 1537228672809129301, 6296488643826193618261, 1611901092819505566274901, 25790417485112089060398421, 6602346876188694799461995861, 27043212804868893898596335048021
Offset: 1
Examples
For n = 1, the first prime number is 2, so a(1) = (4^2-1)/3 = (16-1)/3 = 15/3 = 5; for n = 2, prime(2) = 3, so a(2) = (4^3-1)/3 = (64-1)/3 = 63/3 = 21; for n = 5, prime(5) = 11, so a(5) = (4^(11)-1)/3 = (4194304-1)/3 = 4194303/3 = 1398101.
Crossrefs
Programs
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Java
public static int a(int n){ int p = 1; while(n > 0){ p++; if(!new String(new char[p]).matches("(..+?)\\1+|.?")){ n--; } } return ((int) Math.pow(4, p)-1)/3; } -
Magma
[(4^NthPrime(n) - 1)/3: n in [1..20]]; // Vincenzo Librandi, Oct 17 2018
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Mathematica
a[n_]:=(4^Prime[n] - 1)/3; Array[a, 50] (* Stefano Spezia, Oct 16 2018 *)
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PARI
a(n) = (4^prime(n) - 1)/3; \\ Michel Marcus, Mar 27 2018
Comments