A066700 The leading digits in the terms in A067103 converge; dividing by a suitable power of 10 they converge to the number shown below; sequence gives continued fraction for this number.

1, 2, 12, 4, 34, 1, 22, 1, 4, 1, 1, 2, 1, 1, 17, 16, 3, 1, 1, 2, 1, 1, 1, 5, 1, 1, 3, 3, 14, 2, 107, 1, 1, 8, 5, 4, 7, 1, 4, 1, 6, 3, 19, 3, 1, 1, 2, 3, 5, 76, 1, 1, 2, 1, 1, 90, 2, 2, 48717, 1, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 14, 2, 1, 1, 2, 4, 28, 2, 3, 46, 1, 1, 3, 1, 1, 1, 2, 1, 5, 12, 1, 1, 3, 3, 1, 2, 3, 1, 78, 1, 1, 1, 3, 2, 4, 1, 6, 1, 1, 1048, 1, 3, 1, 1, 2, 3, 4, 1, 2, 4, 3, 8, 1, 12, 5, 1, 1, 7, 1, 11, 11, 1, 118, 6, 1, 2, 1, 5, 3, 1, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2, 3, 5, 4, 1, 12, 147838832589501802758390, 1, 10, 1, 1, 1, 2, 4, 6, 10, 2, 8, 1, 2, 1, 1, 7, 1, 1, 1, 3, 9, 1, 1, 1, 55, 1, 1, 1, 1, 2

Offset: 1

Author

Randall L Rathbun, Jan 12 2002

Keywords

• easy
• cofr
• nonn
• base

Examples

			1.480389426511475059423875475946678140937510326102334419703757169...
		

Crossrefs

Cf. A007908, A019522, A067103.

For a more dramatic continued fraction see A030167.

Programs

PARI

{A067103(n)= c=0; d=0; for(i=1,n, c=c*10^(1+floor(3*log(i)/log(10)))+i^3; d=d*10^(1+floor(log(i)/log(10)))+i; ); floor(c/d) }

PARI

c1(n) = my(s=""); for(k=1, n, s=Str(s, k)); eval(s); \\ A007908
c3(n) = my(s=""); for(k=1, n, s=Str(s, k^3)); eval(s); \\ A019522
lista() = my(nn=1000); default(realprecision, 1000); my(x=c3(nn)\c1(nn)); x = x/10.^(#Str(x)-1); contfrac(x); \\ Michel Marcus, May 25 2022