login
Positions of balanced digits in the decimal expansion of Pi.
3

%I #5 Apr 30 2019 16:41:36

%S 5,155,173,179,210,236,253,262,274,275,293,352,353,359,390,410,468,

%T 603,636,654,661,674,696,703,723,732,764,765,766,767,780,796,804,822,

%U 836,857,875,885,897,918,924,961,981,985,995,996,1015,1059,1200,1234,1246

%N Positions of balanced digits in the decimal expansion of Pi.

%C Cf. A108533 (strong digits), A108534 (weak digits). In the decimal expansion of Pi, balanced digits are much more rare than weak or strong ones.

%t re=RealDigits[N[Pi, 2900]][[1]];b={};Do[r=re[[n]];If[r==(re[[n-1]]+re[[n+1]])/2, b=Append[b, r]], {n, 2, 2899}];A108535=b

%t With[{pid=RealDigits[Pi,10,1300][[1]]},Flatten[Position[Partition[ pid,3,1],_?((#[[1]]+#[[3]])/2==#[[2]]&),1,Heads->False]]]+1 (* _Harvey P. Dale_, Apr 30 2019 *)

%Y Cf. A108533, A108534.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Jun 08 2005