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

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..999

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.

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

Mathematica

Table[Select[FromDigits/@Tuples[{2, 5}, n], Divisible[#, 2^n]&], {n, 18}]//Flatten (* Harvey P. Dale, Oct 12 2022 *)

Crossrefs

Cf. A023398, A050621, A050622, A035014, A055880.

Sequence in context: A299461 A300104 A034311 * A123803 A284767 A101930

Adjacent sequences: A053314 A053315 A053316 * A053318 A053319 A053320

Keyword

base,nonn

Author

Henry Bottomley, Mar 06 2000

Extensions

Formula corrected by Robert Israel, Oct 27 2019

Status

approved