A096060 (2^(p-1)-1)/(3*p) where p = prime(n).

1, 3, 31, 105, 1285, 4599, 60787, 3085465, 11545611, 619094385, 8939118925, 34093383807, 499069107643, 28324525958305, 1628420204246959, 6300117511512825, 367099384551433863, 5542683665339959171

Offset

3,2

Links

T. D. Noe, Table of n, a(n) for n=3..100

P. Terzich, On the Form of Mersenne Numbers, vixra:1202.0024. - From N. J. A. Sloane, Jun 20 2012

Formula

a(n) = A001045(prime(n)-1)/prime(n).

a(n) = A007663(n)/3 for n>2. - Alexander Adamchuk, Jun 08 2006

a(n) = A002450((p-1)/2)/p, for p=prime(n) and n>=3. - Roderick MacPhee, Sep 29 2014

Maple

seq((2^(ithprime(n)-1)-1)/(3*ithprime(n)), n=3..50); # Robert Israel, Oct 14 2014

Mathematica

Table[(2^(Prime[n]-1)-1)/(3*Prime[n]), {n, 3, 22}] (* Alexander Adamchuk, Jun 08 2006 *)
Table[(2^(n-1)-1)/(3n), {n, Prime[Range[3, 20]]}] (* Harvey P. Dale, Dec 27 2014 *)

Prog

(PARI) b(n) = (4^n - 1)/3;
a(n) = p = prime(n); b((p-1)/2)/p; \\ Michel Marcus, Sep 30 2014
(Magma)  [(2^(NthPrime(n)-1)-1) div (3*NthPrime(n)): n in [3..25]]; // Vincenzo Librandi, Oct 15 2014

Crossrefs

Cf. A001045, A002450, A007663.

Sequence in context: A104312 A326736 A107197 * A199367 A295534 A119682

Adjacent sequences: A096057 A096058 A096059 * A096061 A096062 A096063

Keyword

nonn

Author

Amarnath Murthy, Jun 18 2004

Extensions

More terms from Alexander Adamchuk, Jun 08 2006

Formula using A001045 corrected by Jonathan Sondow, Jul 19 2010

Status

approved