A100864 Continued fraction expansion of the square of the constant (A100338) which has the continued fraction equal to A006519 (highest power of 2 dividing n).

1, 1, 4, 1, 74, 1, 8457, 1, 186282390, 1, 1, 1, 2, 1, 430917181166219, 11, 37, 1, 4, 2, 41151315877490090952542206046, 11, 5, 3, 12, 2, 34, 2, 9, 8, 1, 1, 2, 7, 13991468824374967392702752173757116934238293984253807017, 3, 4, 1, 3, 100, 4

Offset: 1

Author

Paul D. Hanna, Nov 21 2004

Keywords

• cofr
• nonn

Comments

Decimal expansion is 1.832967032396... (see A100863). Records are doubly exponential and form A100865.

Links

• Dzmitry Badziahin and Jeffrey Shallit, An Unusual Continued Fraction, arXiv:1505.00667 [math.NT], 2015.
• Dzmitry Badziahin and Jeffrey Shallit, An unusual continued fraction, Proc. Amer. Math. Soc. 144 (2016), 1887-1896.

Crossrefs

Cf. A006519, A100338, A100863, A100865.

Programs

PARI

{CFM=contfracpnqn(vector(650,n,2^valuation(n,2))); contfrac((CFM[1,1]/CFM[2,1])^2,71)}