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 A139474 a(n) = ((2*sqrt(2) + 3)^(2^(prime(n) - 1) - 1) - (3 - 2*sqrt(2))^(2^(prime(n) - 1) - 1))/(4*sqrt(2)). 5

%I #14 Nov 28 2017 06:41:00

%S 1,35,53789260175,300027707381709879256191290532493317737977820735

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

%C Next term a(5) has 783 decimal digits.

%C 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.

%t 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}]

%Y Cf. A001109, A139474, A139475, A139476.

%K nonn

%O 1,2

%A _Artur Jasinski_, Apr 22 2008

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Last modified August 6 00:03 EDT 2024. Contains 374957 sequences. (Running on oeis4.)