A053318 a(n) contains n digits (either '2' or '7') and is divisible by 2^n.

2, 72, 272, 2272, 22272, 222272, 7222272, 27222272, 727222272, 2727222272, 72727222272, 772727222272, 7772727222272, 77772727222272, 277772727222272, 2277772727222272, 72277772727222272, 272277772727222272

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. A023399, 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]+7*10^(n-1)
     fi
od:
seq(A[i],i=1..100); # Robert Israel, Oct 27 2019

Mathematica

Table[Select[FromDigits/@Tuples[{2,7},n],Mod[#,2^n]==0&],{n,18}]//Flatten (* Harvey P. Dale, Jul 14 2025 *)

Formula

a(n) = a(n-1) + 10^(n-1)*(2 + 5*(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 7.

Extensions

Formula corrected by Robert Israel, Oct 27 2019