A053333 a(n) contains n digits (either '4' or '9') and is divisible by 2^n.

4, 44, 944, 4944, 94944, 994944, 4994944, 94994944, 494994944, 9494994944, 49494994944, 449494994944, 9449494994944, 99449494994944, 499449494994944, 9499449494994944, 49499449494994944, 949499449494994944

Offset: 1

Author

Henry Bottomley, Mar 06 2000

Keywords

• base
• nonn

Links

• Ray Chandler, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A023405, A050621, A050622, A035014.

Programs

Mathematica

nxt[{n_,a_}]:=Module[{fd=If[Mod[a,2^(n+1)]==0,4,9]},{n+1,fd 10^IntegerLength[a]+a}]; NestList[ nxt,{1,4},20][[;;,2]] (* Harvey P. Dale, Jul 14 2023 *)

Formula

a(n)=a(n-1)+10^(n-1)*(4+5*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with a 4, if not then n-th term begins with a 9.