A124601 Position of the first 1 in the decimal expansion of the square root of n, or -1 if 1 never appears.

-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

Offset

0,6

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Example

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.

Maple

f:= proc(n) local x, s, j, k;
      if issqr(n) then
         s:= convert(sqrt(n), base, 10);
         for j from 1 to nops(s) do
           if s[-j] = 1 then return j fi
         od;
         return -1
      fi;
      x:= n/100^ilog[100](n);
      s:= floor(sqrt(x));
      if s = 1 then return 1 fi;
      for j from 2 do
        x:= 100*x;
        for k from 1 to 10 do
          if (10*s+k)^2 > x then
            if k = 2 then return j fi;
            s:= 10*s+k-1;
            break
          fi;
        od;
      od
end proc;
map(f, [$0..100]); # Robert Israel, Jan 25 2026

Prog

(PARI)
finddig(n, x)={my(d=digits(n)); for(i=1, #d, if(d[i]==x, return(i))); -1}
a(n) = {if(issquare(n), finddig(sqrtint(n), 1), my(m=2, z=-1); while(z<0, z=finddig(sqrtint(n*100^m), 1); m*=2); z)} \\ Andrew Howroyd, Jan 25 2026

Crossrefs

Sequence in context: A064735 A384439 A104958 * A040508 A305943 A318090

Adjacent sequences: A124598 A124599 A124600 * A124602 A124603 A124604

Keyword

base,easy,sign

Author

Cino Hilliard, Dec 22 2006, corrected Jul 18 2007

Status

approved