A341113 Numerators of continued fraction convergents to 2^(1/12).

1, 1, 17, 18, 89, 196, 1461, 1657, 3118, 7893, 18904, 140221, 579788, 720009, 2019806, 2739815, 166408706, 169148521, 673854269, 843002790, 2359859849, 19721881582, 100969267759, 120691149341, 342351566441, 463042715782, 805394282223, 1268436998005, 7147579272248

Offset: 0

Author

Seiichi Manyama, Feb 05 2021

Keywords

• nonn
• frac

Examples

			Convergents to [1; 16, 1, 4, 2, 7, 1, 1, 2, 2, ...]: 1, 17/16, 18/17, 89/84, 196/185, 1461/1379, 1657/1564, 3118/2943, 7893/7450, 18904/17843, ...
		

Links

• Eric Weisstein's World of Mathematics, Continued Fraction

Crossrefs

For denominators see A341114.

Cf. A001333, A010774, A103922.

Programs

Mathematica

Join[{1}, Numerator[Convergents[2^(1/12), 28]]] (* Amiram Eldar, Apr 28 2021 *)

Formula

a(0) = 1, a(1) = 1, a(n) = A103922(n-1) * a(n-1) + a(n-2) for n >1.