A175389 Smallest nonnegative number k such that 2^k contains n, 2n and 3n as substrings of its decimal expansion.

10, 17, 18, 29, 50, 87, 86, 31, 70, 62, 101, 147, 86, 124, 93, 144, 82, 81, 157, 113, 100, 110, 146, 110, 88, 96, 141, 158, 94, 69, 79, 75, 123, 244, 192, 297, 181, 168, 128, 255, 101, 140, 197, 182, 147, 228, 111, 189, 224, 303, 288, 510, 321, 289, 232, 432, 342

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Example

2^10 = 1024 is the smallest power of 2 containing a 0, so a(0) = 10.
2^101 = 2535301200456458802993406410752 is the smallest power of 2 containing 10, 20, and 30 as substrings, so a(10) = 101.

Maple

N:= 100: # to get a(0) to a(N)
R:= 'R': count:= 0:
for k from 0 while count < N+1 do
   t:= 2^k;
   d:= ilog10(t);
   V:= select(`<=`, {seq(seq(floor(t/10^i) mod 10^j, j=1..d+1-i),
      i=0..d)}, 3*N);
   V3:= select(t -> t <= N and has(V, 2*t) and has(V, 3*t), V);
   for v in V3 do
     if not assigned(R[v]) then
       count:= count+1;
       R[v]:= k;
     fi
   od;
od:
seq(R[n], n=0..N); # Robert Israel, Jul 19 2016

Mathematica

Table[SelectFirst[Range[0, 10^3], Function[k, Length@ DeleteCases[
Map[SequencePosition[IntegerDigits[2^k], IntegerDigits@ #] &, n Range@ 3] /. {} -> 0, m_ /; m == 0] == 3]], {n, 0, 56}] (* Michael De Vlieger, Jul 19 2016, Version 10.1 *)

Crossrefs

Cf. A030000 (Susanna's sequence: smallest nonnegative number k such that 2^k contains n).

Sequence in context: A176664 A256346 A079630 * A350779 A280591 A308691

Adjacent sequences: A175386 A175387 A175388 * A175390 A175391 A175392

Keyword

base,nonn

Author

Zak Seidov, Apr 27 2010

Status

approved