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

Author

Zak Seidov, Apr 27 2010

Keywords

• base
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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 *)