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A220426 Least nonsquare whose square root starts with at least n even decimal digits. 3
2, 5, 5, 6, 8, 8, 8, 18, 18, 18, 1652, 2135, 40332, 40332, 78740, 80661, 165389, 165389, 239008, 686015, 4260196, 5018507, 5018507, 5018507, 5018507, 43624023, 43624023, 43624023, 43624023, 43624023, 1801833064, 1801833064, 1801833064, 1801833064, 1801833064 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..43

EXAMPLE

a(0) = 2 because sqrt(2) = 1.41... starts with 0 even digits, and is the smallest nonsquare for which this is the case.

a(1) = a(2) = 5 because sqrt(5) = 2.23... starts with at least 1 even digit, in fact 2 even digits, whereas sqrt(3) starts off with an odd digit.

a(3) = 6 because sqrt(6) = 2.449... starts off with 3 even digits.

MAPLE

nexteven:= proc(x)

   local d;

   for d from 0 while x mod 10^(d+1) = 8*(10^(d+1)-1)/9 do od:

   x - 8*(10^(d)-1)/9 + 2*10^(d)

end proc;

evendigits:= proc(x)

local n0, n, d, s;

n0:= ilog10(x);

if type(n0, odd) then n0:= n0-1 end if;

for n from 0 do

   d:= floor(x/10^(n0-2*n));

   s:= floor(sqrt(d));

   while not type(s, integer) do

    Digits:= Digits+2; s:= floor(sqrt(d))

   end do;

   if type(s mod 10, odd) then return n end if;

end do;

end proc;

y:= 2: bsf:= 0: R[0]:= 2:

while bsf < 20 do

   for x from y^2+1 to (y+1)^2-1 do

      v:= evendigits(x);

      if v > bsf then

        for j from bsf+1 to v do R[j]:= x end do;

        bsf:= v;

      end if;

    end do;

   y:= nexteven(y);

end do:

  seq(R[n], n=0..bsf);

MATHEMATICA

f[n_] := Block[{s = Split[ Boole[ EvenQ@# & /@ RealDigits[Sqrt@ n, 10, 32][[1]]]][[1]]}, If[IntegerQ@ Sqrt@ n || Union@ s == {0}, -1, Length@ s]] (* Robert G. Wilson v, Dec 15 2012 *)

PROG

(PARI) a(n) = {my(g=10^(n-1), v); for(k=2, oo, if(setintersect([0, 2, 4, 6, 8], v=Set(digits(floor(sqrt(k)*g))[1..n]))==v && !issquare(k), return(k))); } \\ Jinyuan Wang, Apr 16 2020

CROSSREFS

Cf. A210492.

Sequence in context: A130856 A004095 A145434 * A117899 A120839 A332525

Adjacent sequences:  A220423 A220424 A220425 * A220427 A220428 A220429

KEYWORD

nonn,base

AUTHOR

Robert Israel, Dec 14 2012

EXTENSIONS

a(21)-a(29) from Robert G. Wilson v, Dec 15 2012

a(30)-a(34) from Jinyuan Wang, Apr 16 2020

STATUS

approved

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Last modified June 21 03:51 EDT 2021. Contains 345354 sequences. (Running on oeis4.)