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

0,1

Comments

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

Links

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

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A182685 A182686 A369823 * A223601 A186490 A223694

Adjacent sequences: A176765 A176766 A176767 * A176769 A176770 A176771

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Apr 25 2010

Extensions

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

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

Status

approved