A176768 Smallest power of 8 whose decimal expansion contains n.

4096, 1, 512, 32768, 64, 512, 64, 32768, 8, 4096, 1073741824, 4398046511104, 512, 134217728, 262144, 2097152, 16777216, 134217728, 1073741824, 68719476736, 2097152, 262144, 2251799813685248, 9223372036854775808, 1073741824

Offset: 0

Author

Jonathan Vos Post, Apr 25 2010

Keywords

• base
• easy
• nonn

Comments

This is to 8 as A176763 is to 3 and as A030001 is to 2.

Examples

			a(1) = 1 because 8^0 = 1 has "1" as a substring (not a proper substring, though).
a(2) = 512 because 8^3 = 512 has "2" as a substring.
a(3) = 32768 because 8^5 = 32768 has "3" as a substring.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..9999

Crossrefs

Cf. A001018, A030001, A176763, A176764-A176773.

Programs

Maple

F:= proc(dmax) local R,count,x,N,L,d,i,v;
count:= 0: x:= 1/8: N:= 10^dmax:
while count < N do
  x:= 8*x;
  L:= convert(x,base,10);
  for d from 1 to min(dmax, nops(L)) do
    for i from 1 to nops(L)-d+1 do
      v:= add(L[j]*10^(j-i),j=i..i+d-1);
      if not assigned(R[v]) then count:= count+1; R[v]:= x fi
od od od:
seq(R[v],v=0..N-1);
end proc:
F(2); # Robert Israel, Dec 25 2019

Mathematica

A176768[n_] := Block[{k = -1}, While[StringFreeQ[IntegerString[8^++k], IntegerString[n]]]; 8^k]; Array[A176768, 50, 0] (* Paolo Xausa, Apr 04 2024 *)

Formula

a(n) = MIN{A001018(i) such that n in decimal representation is a substring of A001018(i)}.

a(n) = 8^A062525(n). - Michel Marcus, Sep 30 2014

Extensions

More terms from Sean A. Irvine and Jon E. Schoenfield, May 05 2010

a(0)=4096 inserted by Robert Israel, Dec 25 2019