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
Examples
1.480389426511475059423875475946678140937510326102334419703757169...
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