A139474 a(n) = ((2*sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2*sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)).

1, 35, 53789260175, 300027707381709879256191290532493317737977820735

Offset: 1

Author

Artur Jasinski, Apr 22 2008

Keywords

• nonn

Comments

Next term a(5) has 783 decimal digits.

Conjecture of Kenneth J Ramsey from May 16 2006 (see A001109): a(n) is divisible by 2^prime(n)-1 if and only 2^prime(n)-1 is a Mersenne prime.

Crossrefs

Cf. A001109, A139474, A139475, A139476.

Programs

Mathematica

Table[Expand[((2*Sqrt[2] + 3)^(2^(Prime[n] - 1) - 1) - (3 - 2*Sqrt[2])^(2^(Prime[n] - 1) - 1))/(4*Sqrt[2])], {n, 1, 10}]