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

1,3

Comments

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

Links

Table of n, a(n) for n=1..41.

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.

Prog

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

Crossrefs

Cf. A006519, A100338, A100863, A100865.

Sequence in context: A173008 A298828 A114917 * A295178 A255192 A299582

Adjacent sequences: A100861 A100862 A100863 * A100865 A100866 A100867

Keyword

cofr,nonn

Author

Paul D. Hanna, Nov 21 2004

Status

approved