A261532 Hall's sequence g_n.

7, 589, 11064985, 7835767761026353, 7859104819806710982081319640824417, 15811975313589523224392147529414564125936123169432771986649715567359169

Offset: 3

Author

Joerg Arndt, Aug 24 2015

Keywords

• nonn

Links

• James S. Hall, A remark on the primeness of Mersenne numbers, J. London Math. Soc. 28, (1953), 285-287.

Crossrefs

Cf. A002812, A003010.

Programs

Magma

[n le 1 select 7 else 2*(Self(n-1)-1)*(1+2^(n+1)*(Self(n-1)-1)) + 1: n in [1..6]]; // Vincenzo Librandi, Aug 24 2015

PARI

N=11;  g=vector(N);  g[3] = 7;
for (n=3, N-1, g[n+1] = 2*(g[n]-1)*(1+2^n*(g[n]-1))+1 );
vector(N-3, j, g[j+2])

Formula

a(n) = g(n) where g(3) = 7 and g(n+1) = 2*(g(n)-1)*(1+2^n*(g(n)-1)) + 1.