A259929 Value of DIS (Decimal Integer Series) constant based on the sequence of cubes.

1, 0, 1, 6, 7, 9, 7, 7, 3, 8, 2, 7, 6, 8, 8, 8, 1, 7, 7, 0, 4, 4, 6, 3, 7, 4, 7, 3, 1, 6, 2, 4, 5, 5, 4, 3, 5, 5, 6, 6, 8, 8, 2, 7, 7, 5, 1, 2, 3, 4, 7, 3, 8, 7, 2, 6, 3, 1, 9, 3, 0, 6, 2, 0, 8, 3, 1, 7, 5, 5, 0, 9, 8, 4, 4, 0, 6, 3, 9, 0, 4, 0, 9, 9, 8, 6, 0, 8, 0, 6, 8, 8, 3, 3, 9, 9, 8, 2, 4, 7

Offset: 0

Author

R. J. Mathar, Jul 09 2015

Keywords

• nonn
• cons
• base

Examples

			Equals 0.10167977382768881770446374731...
		

Crossrefs

Cf. A258718, A259838.

Programs

Maple

Digits := 220 ;
x := 0.0 ;
for ndigs from 1 to 200 do
    # 10^(ndigs-1)<= n^3  < 10^ndigs
    nmin := ceil(10^((ndigs-1)/3)) ;
    nmax := floor( root[3](10^(ndigs)-1) ) ;
    if nmax >= nmin then
        # sum nmin^3.. nmax^3
        csu := A000537(nmax)-A000537(nmin-1) ;
        x := x+evalf(csu/100^ndigs) ;
        printf("%.120f\n",x) ;
    end if;
end do:

Formula

Equals sum_{n>=1} c/100^A055642(c) where c=A000578(n).