A053334 a(n) contains n digits (either '1' or '6') and is divisible by 2^n.
6, 16, 616, 1616, 11616, 111616, 6111616, 16111616, 616111616, 1616111616, 61616111616, 661616111616, 1661616111616, 61661616111616, 661661616111616, 6661661616111616, 66661661616111616, 666661661616111616
Offset: 1
Links
- Ray Chandler, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
nxt[{n_,a_}]:={n+1,a+10^n (6-5*Mod[a/2^n,2])}; NestList[nxt,{1,6},20][[;;,2]] (* Harvey P. Dale, Aug 20 2025 *)
Formula
a(n)=a(n-1)+10^(n-1)*(6-5*[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 6, if not then n-th term begins with a 1.