A322645 Number of times the digit 4 appears in the first 10^n decimal digits of sqrt(2), sometimes called Pythagoras's constant, counting after the decimal point.

2, 9, 100, 1016, 10100, 100024, 1000126, 10000054, 100012725, 1000008724

Offset

1,1

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

Table of n, a(n) for n=1..10.

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]="4" then C:=C+1; fi;
  od;
  return(C);
end;

Mathematica

Table[DigitCount[IntegerPart[(Sqrt[2]-1)*10^10^n], 10, 4], {n, 1, 10}] (* Robert Price, Mar 29 2019 *)

Crossrefs

Cf. A002193, A099294, A322641, A322642, A322643, A322644, A322646, A322647, A322648. A322649, A322650.

Sequence in context: A360696 A357825 A187647 * A368725 A277180 A013520

Adjacent sequences: A322642 A322643 A322644 * A322646 A322647 A322648

Keyword

nonn,base,more

Author

Martin Renner, Dec 21 2018

Status

approved