A289491 a(n) = denominator of 1/(1 + 1/(1 + 2/(1 + ... (1 + n)))).

2, 4, 5, 13, 19, 58, 191, 131, 1187, 2231, 17519, 71063, 29881, 323423, 2887921, 13237457, 2397389, 15030317, 742458253, 3748521653, 9670072483, 25451905333, 10932619111, 78684575461, 4163946939067, 11799518538967, 136025604432743, 159359728522979

Offset: 1

Author

Seiichi Manyama, Sep 02 2017

Keywords

• nonn
• frac

Examples

			1/2, 3/4, 3/5, 9/13, 12/19, 39/58, 123/191, 87/131, 771/1187, 1473/2231, 11427/17519, 46779/71063, 19533/29881, ... = A225436/A289491 -> A108088.
A225436(1)/a(1) = 1/2  = 1/(1 + 1)                         =  1/2,
A225436(2)/a(2) = 3/4  = 1/(1 + 1/(1 + 2))                 =  3/4,
A225436(3)/a(3) = 3/5  = 1/(1 + 1/(1 + 2/(1 + 3)))         =  6/10,
A225436(4)/a(4) = 9/13 = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4)))) = 18/26.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..843
• OEIS Wiki, A remarkable formula of Ramanujan

Crossrefs

Cf. A000085, A000932, A108088, A225435, A225436 (numerators).

Programs

Maple

p:= (i, n)-> `if`(i=n, (1+n), 1+i/p(i+1,n)):
a:= n-> denom(1/p(1,n)):
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 02 2017

Formula

a(n) = A225435(n) + A225436(n).

A225436(n)/a(n) = 1/(1 + 1/(1 + 2/(1 + ... (1 + n)))) = A000932(n)/A000085(n+1).