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A243972 Least number k such that 2^k contains exactly n identical digits. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A064804

Adjacent sequences:  A243969 A243970 A243971 * A243973 A243974 A243975

KEYWORD

nonn,base

AUTHOR

Derek Orr, Jun 16 2014

STATUS

approved

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Last modified January 19 14:53 EST 2020. Contains 331049 sequences. (Running on oeis4.)