A078976 Numerator of n-th convergent to e^(2/3).

1, 2, 37, 261, 298, 559, 5888, 318511, 5102064, 5420575, 10522639, 205350716, 18492087079, 462507527691, 480999614770, 943507142461, 26899199603678, 3390242657205889, 115295149544603904, 118685392201809793, 233980541746413697, 8775965436819116582, 1421940381306443299981

Offset: 1

Author

Benoit Cloitre, Dec 19 2002

Keywords

• frac
• nonn

Crossrefs

Cf. A069951, A001518, A007676, A078977 (denominators).

Programs

Mathematica

Convergents[Exp[2/3], 25] // Numerator (* Amiram Eldar, May 09 2025 *)

PARI

default(realprecision,100); /* large enough */
a(n)=contfracpnqn(contfrac(exp(2/3), n))[1,1]
vector(30,n,a(n))

Formula

Special cases : a(5k+1) = A001518(3k); a(5k+3) = A001518(3k+2).