A070900 a(0)=1, a(n) is the smallest integer >= a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(0)+1/a(1)+1/a(2)+...+1/a(n) equals the number of elements in this continued fraction.

1, 2, 4, 10, 32, 44, 47, 56, 61, 249, 261, 379, 410, 418, 418, 457, 554, 576, 938, 1262, 1524, 1636, 1813, 1817, 1849, 1851, 1914, 2127, 2192, 2243, 2345, 2413, 2511, 2579, 2722, 2777, 2939, 3002, 3309, 3361, 3504, 4178, 4404, 4911, 6088, 8623, 9104, 9468

Offset

0,2

Comments

Sum_{k>=0} 1/a(k) = C = 1.99...

Links

Table of n, a(n) for n=0..47.

Example

The continued fraction for S(11)=1+1/2+1/4+1/10+1/32+1/44+1/47+1/56+1/61+1/249+1/261+1/379 is [1, 1, 32, 3, 10, 6, 1, 1, 1, 8, 1, 1, 1, 1, 2, 1, 9, 3, 1, 1, 2, 23, 3, 1, 1, 2, 1, 21, 1, 1, 5, 3] which contains 32 elements and with largest element 32.

Prog

(PARI) s=1; t=1; for(n=1, 60, s=s+1/t; while(abs(length(contfrac(s+1/t))-vecmax(contfrac(s+1/t)))>0, t++); print1(t, ", "))

Crossrefs

Sequence in context: A005268 A243931 A005269 * A296003 A263662 A151400

Adjacent sequences: A070897 A070898 A070899 * A070901 A070902 A070903

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Extensions

Name corrected by Sean A. Irvine, Jun 18 2024

Status

approved