A091942 a(n) equals the maximum number of partial quotients in the simple continued fraction expansion of (1/n + 1/k) for k>=1.

2, 6, 7, 8, 9, 9, 11, 11, 12, 11, 12, 14, 13, 13, 13, 13, 14, 13, 13, 14, 15, 14, 14, 14, 14, 15, 14, 15, 15, 15, 16, 16, 16, 17, 15, 16, 16, 16, 17, 15, 17, 17, 17, 16, 16, 17, 17, 17, 17, 17, 17, 17, 18, 16, 19, 17, 19, 18, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 18, 19, 18

Offset

1,1

Links

Table of n, a(n) for n=1..71.

Formula

a(n) = length(contfrac(1/A091941(n) + 1/n)).

Prog

(PARI) {a(n)=local(A); M=0; for(k=2*n^2-1, 3*n^2, L=length(contfrac(1/k+1/n)); if(L>M, M=L; A=M)); A}

Crossrefs

Cf. A091941, A091943, A091944.

Sequence in context: A186504 A096909 A073005 * A372591 A047555 A184939

Adjacent sequences: A091939 A091940 A091941 * A091943 A091944 A091945

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2004

Status

approved