A053317 a(n) contains n digits (either '2' or '5') and is divisible by 2^n.
2, 52, 552, 5552, 55552, 255552, 5255552, 55255552, 255255552, 2255255552, 22255255552, 222255255552, 5222255255552, 55222255255552, 255222255255552, 2255222255255552, 22255222255255552, 222255222255255552
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..999
Programs
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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]+5*10^(n-1) fi od: seq(A[i],i=1..100); # Robert Israel, Oct 27 2019
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Mathematica
Table[Select[FromDigits/@Tuples[{2,5},n],Divisible[#,2^n]&],{n,18}]//Flatten (* Harvey P. Dale, Oct 12 2022 *)
Formula
a(n) = a(n-1) + 10^(n-1)*(2 + 3*(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 5.
Extensions
Formula corrected by Robert Israel, Oct 27 2019