A124686 Position of the first 1 in the decimal expansion of the cube root of n, or -1 if this digit never appears.

-1, 1, 1, 1, 1, 1, 1, 1, -1, 13, 2, 15, 11, 4, 3, 6, 3, 4, 7, 7, 3, 8, 17, 13, 8, 6, 26, -1, 10, 6, 2, 2, 2, 24, 6, 4, 4, 7, 4, 4, 3, 6, 27, 17, 20, 23, 10, 11, 7, 9, 7, 14, 6, 13, 8, 13, 44, 7, 21, 9, 3, 8, 7, 16, -1, 27, 4, 4, 4, 2, 2, 2, 2, 2, 2, 3, 17, 11, 10, 17, 21, 9, 7, 10, 6, 11, 3, 4, 8, 28, 4, 7, 3, 45, 22, 35, 12, 38, 3, 11, 4

Offset

0,10

Links

Chai Wah Wu, Table of n, a(n) for n = 0..10000

Mathematica

Off[First::first]; Flatten[Table[First[Position[RealDigits[n^(1/3), 10, 120] [[1]], 1]], {n, 0, 100}]/.First[{}]->-1] (* Harvey P. Dale, May 05 2012 *)(* to restore the error message, enter "On[First::first]" after running the program *)

Prog

(PARI) digitposcbrt(n, m) = \ cbrt expansion { local(x, y, r, dot); for(x=0, n, r = (x^(1/3)); if(iscube(x), y=find(Str(floor(r)), m), y=find(Str(r), m); dot=find(Str(r), "."); if(dot < y, y--); ); if(y, print1(y", "), print1(-1", ") ) ) } find(str, match) = \Return the position of the first occurrence of string \match in string str { local(lnm, lns, x, c, i); str=Str(str); \This allows leaving quotes off input match=Str(match); c=0; i=0; lns=length(str); lnm=length(match); if(lnm>1, i=1); x=1; while(x<=lns-lnm+1, if(mid(str, x, lnm)== match, break, x++); ); if(x>lns, return(0), return(x)) } mid(str, s, n) = \ Get a substring of length n from string str starting at position s in str. { local(v, ln, x, tmp); v =""; tmp = Vec(str); ln=length(tmp); for(x=s, s+n-1, v=concat(v, tmp[x]); ); return(v) } iscube(n) = { local(r); r = n^(1/3); if(floor(r+.5)^3== n, 1, 0) }

Crossrefs

Sequence in context: A298059 A298708 A367936 * A113807 A008832 A180704

Adjacent sequences: A124683 A124684 A124685 * A124687 A124688 A124689

Keyword

base,easy,sign

Author

Cino Hilliard, Dec 24 2006

Status

approved