A243972 Least number k such that 2^k contains exactly n identical digits.

1, 16, 22, 23, 53, 70, 74, 93, 122, 147, 156, 167, 168, 222, 214, 221, 283, 315, 311, 312, 313, 314, 426, 466, 427, 474, 439, 563, 630, 576, 554, 575, 626, 627, 793, 722, 809, 766, 861, 889, 925, 893, 989, 890, 1077, 891, 983, 892, 1130, 1128, 1135, 1134, 1217, 1129, 1238

Offset

1,2

Comments

The terms are not all unique: thus a(491) = a(497) = 14705. - Robert Israel, May 26 2017

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Index entries for sequences related to decimal expansion of n

Example

2**22 = 4194304 contains exactly 3 of the same digit (4). Since 22 is the smallest power of 2 to have this, a(3) = 22.

Maple

N:= 100: # To get a(1)..a(N)
Agenda:= {$1..N}:
for n from 1 while nops(Agenda) > 0 do
  S:= convert(2^n, base, 10);
  V:= Vector(10);
  for s in S do V[s+1]:= V[s+1]+1 od:
  T:= convert(V, set) intersect Agenda;
  for t in T do A[t]:= n od:
  Agenda:= Agenda minus T;
od:
seq(A[i], i=1..N); # Robert Israel, May 26 2017

Prog

(Python)
def b():
..n = 1
..k = 1
..while k < 50000:
....st = str(2**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. A000079, A243975.

Sequence in context: A123662 A065778 A305944 * A091118 A294125 A360735

Adjacent sequences: A243969 A243970 A243971 * A243973 A243974 A243975

Keyword

nonn,base

Author

Derek Orr, Jun 16 2014

Status

approved