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A124601
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Position of the first 1 in the decimal expansion of the square root of n, or -1 if 1 never appears.
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0
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-1, 1, 1, 1, -1, 23, 14, 7, 8, -1, 2, 3, 5, 7, 4, 15, -1, 2, 11, 25, 5, 26, 6, 7, 17, -1, 6, 2, 4, 5, 13, 16, 17, 24, 7, 3, -1, 15, 2, 26, 41, 5, 57, 23, 12, 25, 11, 13, 17, -1, 4, 2, 3, 5, 22, 3, 6, 32, 3, 4, 12, 3, 12, 11, -1, 24, 2, 2, 6, 12, 22, 5, 7, 12, 19, 25, 3, 14, 4, 5, 7
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OFFSET
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0,6
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LINKS
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EXAMPLE
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For n=5, the concatenated digits of sqrt(5) are 223606797749978969640917366... The digit 1 first occurs in the 23rd position of this string of digits. So 23 is the 6th entry in the table counting from the 0th entry.
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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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