A053336 a(n) contains n digits (either '5' or '6') and is divisible by 2^n.

6, 56, 656, 6656, 66656, 566656, 6566656, 66566656, 666566656, 6666566656, 56666566656, 656666566656, 6656666566656, 66656666566656, 566656666566656, 6566656666566656, 56566656666566656, 556566656666566656

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. A023408, A050621, A050622, A035014.

Programs

Mathematica

Block[{a = {6}, k, m, w}, Do[k = 1; If[Mod[a[[-1]], 2^i] == 0, Set[w, Prepend[ConstantArray[5, i - 1], 6]], Set[w, ConstantArray[5, i]]]; While[Mod[Set[m, FromDigits[w + PadLeft[IntegerDigits[k, 2], i]]], 2^i] != 0, k++]; AppendTo[a, m], {i, 2, 18}]; a] (* Michael De Vlieger, Dec 10 2020 *)

Formula

a(n) = a(n-1)+10^(n-1)*(6-[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 5.

Conjecture: a(n) = 10^n - A035014(n). - J. Lowell, Nov 16 2020