A053314 a(n) contains n digits (either '1' or '4') and is divisible by 2^n.

4, 44, 144, 4144, 14144, 414144, 1414144, 41414144, 441414144, 1441414144, 11441414144, 411441414144, 4411441414144, 44411441414144, 444411441414144, 1444411441414144, 41444411441414144, 441444411441414144

Offset: 1

Author

Henry Bottomley, Mar 06 2000

Keywords

• base
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..999

Crossrefs

Cf. A023401, A050621, A050622, A035014.

Programs

Maple

A[1]:= 4:
for n from 2 to 100 do
   if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+4*10^(n-1)
   else A[n]:= A[n-1]+10^(n-1)
fi
od:
seq(A[i],i=1..100); # Robert Israel, Oct 27 2019

Mathematica

nxt[{n_,a_}]:={n+1,If[Divisible[a,2^(n+1)],4*10^IntegerLength[a]+ a, 10^IntegerLength[ a]+a]}; NestList[nxt,{1,4},20][[All,2]] (* Harvey P. Dale, Oct 30 2022 *)

Formula

a(n) = a(n-1) + 10^(n-1)*(4 - 3*(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 1.

Extensions

Formula corrected by Robert Israel, Oct 27 2019