A053316 a(n) contains n digits (either '2' or '3') and is divisible by 2^n.

2, 32, 232, 3232, 23232, 223232, 2223232, 32223232, 232223232, 3232223232, 23232223232, 323232223232, 3323232223232, 23323232223232, 323323232223232, 3323323232223232, 33323323232223232, 333323323232223232

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. A023397, A050621, A050622, A035014.

Programs

Maple

A[1]:= 2:
for n from 2 to 100 do
   if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+2*10^(n-1)
   else A[n]:= A[n-1]+3*10^(n-1)
     fi
od:
seq(A[i],i=1..100); # Robert Israel, Oct 27 2019

Formula

a(n) = a(n-1) + 10^(n-1)*(2 + (a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if a(n-1) is divisible by 2^n then a(n) begins with a 2, if not then a(n) begins with a 3.

Extensions

Formula corrected by Robert Israel, Oct 27 2019