%I #13 Feb 16 2025 08:33:57
%S 2,8,109,1004,9876,100436,1000208,9998091,99995645,999987069
%N Number of times the digit 2 appears in the first 10^n decimal digits of sqrt(2), sometimes called Pythagoras's constant, counting after the decimal point.
%C 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.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PythagorassConstantDigits.html">Pythagoras's Constant Digits</a>.
%p a:=proc(n)
%p local digits, SQRT2, C, i;
%p digits:=10^n+100;
%p SQRT2:=convert(frac(evalf[digits](sqrt(2))),string)[2..digits-99];
%p C:=0;
%p for i from 1 to length(SQRT2) do
%p if SQRT2[i]="2" then C:=C+1; fi;
%p od;
%p return(C);
%p end;
%t Table[DigitCount[IntegerPart[(Sqrt[2]-1)*10^10^n], 10, 2], {n,1,10}] (* _Robert Price_, Mar 29 2019 *)
%Y Cf. A002193, A099293, A322641, A322642, A322644, A322645, A322646, A322647, A322648, A322649, A322650.
%K nonn,base,more,changed
%O 1,1
%A _Martin Renner_, Dec 21 2018