login
A322650
Number of times the digit 9 appears in the first 10^n decimal digits of sqrt(2), sometimes called Pythagoras's constant, counting after the decimal point.
10
0, 8, 92, 1019, 9945, 100121, 1000566, 10000056, 99996852, 999989494
OFFSET
1,2
COMMENTS
It is not known if sqrt(2) is normal, but the distribution of decimal digits found for the first 10^n digits of sqrt(2) shows no statistically significant departure from a uniform distribution.
LINKS
Eric Weisstein's World of Mathematics, Pythagoras's Constant Digits.
MAPLE
a:=proc(n)
local digits, SQRT2, C, i;
digits:=10^n+100;
SQRT2:=convert(frac(evalf[digits](sqrt(2))), string)[2..digits-99];
C:=0;
for i from 1 to length(SQRT2) do
if SQRT2[i]="9" then C:=C+1; fi;
od;
return(C);
end;
MATHEMATICA
Table[DigitCount[IntegerPart[(Sqrt[2]-1)*10^10^n], 10, 9], {n, 1, 10}] (* Robert Price, Mar 29 2019 *)
KEYWORD
nonn,base,more
AUTHOR
Martin Renner, Dec 21 2018
STATUS
approved