A243975 Least number k such that 3^k contains exactly n identical digits.

1, 8, 11, 29, 32, 47, 34, 33, 90, 98, 112, 136, 128, 172, 111, 168, 146, 211, 241, 218, 220, 290, 278, 298, 323, 355, 329, 316, 344, 446, 427, 395, 410, 528, 481, 443, 498, 523, 574, 540, 531, 538, 618, 549, 694, 669, 733, 717, 788, 707, 740, 734, 831, 743, 857, 850, 864

Offset

1,2

Comments

It is permissible for 3^k to have more than one digit repeated n times. For example a(11)=112, and 3^112 has 11 digits equal to 3 and also 11 digits equal to 7. - Harvey P. Dale, Feb 19 2015

Links

Table of n, a(n) for n=1..57.

Index entries for sequences related to decimal expansion of n

Example

3^11 = 177147 contains 3 of the same digit (7). Since 11 is the smallest power of 3 to do this, a(3) = 11.

Maple

N:= 1000: # to get a(1) to a(m-1) where a(m) is the first > N
f:= proc(k)
  local L;
  L:= convert(3^k, base, 10);
  max(seq(numboccur(i, L), i=0..9));
end proc:
for k from 1 to N do
  v:= f(k);
  if not assigned(A[v]) then A[v]:= k fi;
od:
for m from 1 while assigned(A[m]) do od:
seq(A[i], i=1..m-1); # Robert Israel, Feb 19 2015

Mathematica

lnk[n_]:=Module[{k=1}, While[Count[DigitCount[3^k], n]<1, k++]; k]; Array[ lnk, 60] (* Harvey P. Dale, Feb 19 2015 *)

Prog

(Python)
def b():
..n = 1
..k = 1
..while k < 50000:
....st = str(3**k)
....if len(st) >= n:
......for a in range(10):
........count = 0
........for i in range(len(st)):
..........if st[i] == str(a):
............count += 1
........if count == n:
..........print(k, end=', ')
..........n += 1
..........k = 0
..........break
......k += 1
....else:
......k += 1
b()

Crossrefs

Cf. A000244, A243972.

Sequence in context: A053701 A029615 A051791 * A160796 A160416 A056873

Adjacent sequences: A243972 A243973 A243974 * A243976 A243977 A243978

Keyword

nonn,base

Author

Derek Orr, Jun 16 2014

Status

approved