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A124600
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Position of the first 0 in the decimal expansion of the square root of n, or -1 if 0 never appears.
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0
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1, -1, 14, 5, -1, 5, 17, 11, 16, -1, 10, 10, 6, 3, 36, 12, -1, 6, 7, 13, 37, 16, 4, 26, 52, -1, 2, 12, 6, 9, 11, 13, 16, 14, 4, 5, -1, 2, 8, 18, 10, 3, 4, 12, 10, 3, 20, 9, 6, -1, 2, 48, 6, 4, 49, 11, 32, 13, 9, 15, 19, 4, 5, 21, -1, 2, 5, 24, 17, 3, 6, 19, 16, 5, 3, 4, 11, 17, 7, 19, 9
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OFFSET
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0,3
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COMMENTS
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The real 0's representations after the decimal point of the expansion of the square root of perfect squares are ignored. In other words for sqrt(4) = 2.0000..., the trailing 0's are ignored.
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LINKS
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EXAMPLE
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For n=14, the concatenated digits of sqrt(14) are The digit 0 in the 36th position of this string of digits so 36 is the 15th entry the table counting from the 0th entry.
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MATHEMATICA
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Join[{1}, Table[If[IntegerQ[Sqrt[n]], {{-1, -1}}, SequencePosition[ RealDigits[ Sqrt[n], 10, 100][[1]], {0}, 1]], {n, 100}][[All, 1]][[All, 1]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 02 2016 *)
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PROG
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(PARI) digitpos(n, m) = /* m-th digit in sqrt expansions */ { local(x, y, r, dot); default(realprecision, 1000); for(x=0, n, r = sqrt(x); if(issquare(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) = /* Revised 2007 */ { local(lnm, lns, tstr, vstr, x, j); vstr=Vec(Str(str)); match=Str(match); lns=length(str); lnm=length(match); for(x=1, lns-lnm+1, tstr=""; for(j=x, x+lnm-1, tstr=concat(tstr, vstr[j]); ); if(match==tstr, return(x)) ); return(0); }
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CROSSREFS
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KEYWORD
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base,easy,sign
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AUTHOR
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STATUS
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approved
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