A059918 a(n) = (3^(2^n)-1)/2.

1, 4, 40, 3280, 21523360, 926510094425920, 1716841910146256242328924544640, 5895092288869291585760436430706259332839105796137920554548480

Offset: 0

Author

Henry Bottomley, Feb 08 2001

Keywords

• nonn
• easy

Comments

Denominator of b(n) where b(n) = 1/2*(b(n-1) + 1/b(n-1)), b(0)=2. - Vladeta Jovovic, Aug 15 2002

Links

• Harry J. Smith, Table of n, a(n) for n = 0..11

Crossrefs

Cf. A059917 (numerators).

Cf. A059723, A059917, A059919, A011764.

Cf. A007089, A136308.

Programs

Mathematica

Array[(3^(2^#) - 1)/2 &, 8, 0] (* Michael De Vlieger, Feb 05 2022 *)

PARI

{ for (n=0, 11, write("b059918.txt", n, " ", (3^(2^n) - 1)/2); ) } \\ Harry J. Smith, Jun 30 2009

Formula

a(n) = a(n-1)*(3^(2^(n-1))+1) with a(0) = 1.

a(n) = (3^(2^n)-1)/2 = (A059723(n+1)-A059723(n))/A059723(n) = A059917(n)-1 = a(n-1)*A059919(n-1) = a(n-1)*(A011764(n-1)+1)

1 = Sum_{n>=0} 3^(2^n)/a(n+1). 1 = 3/4 + 9/40 + 81/3280 + 6561/21523360 + ...; with partial sums: 3/4, 39/40, 3279/3280, 21523359/21523360, ..., (a(n)-1)/a(n), ... . - Gary W. Adamson, Jun 22 2003

A136308(n) = A007089(a(n)). - Jason Kimberley, Dec 19 2012