A053315 a(n) contains n digits (either '4' or '5') and is divisible by 2^n.

4, 44, 544, 4544, 44544, 444544, 4444544, 54444544, 454444544, 5454444544, 45454444544, 545454444544, 5545454444544, 55545454444544, 555545454444544, 4555545454444544, 44555545454444544, 544555545454444544

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. A023403, 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]+5*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)*(4 + (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 5.

Extensions

Formula corrected by Robert Israel, Oct 27 2019