A137214 a(n) is the number of distinct decimal digits in 2^n.
1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 3, 5, 4, 4, 7, 6, 5, 4, 4, 4, 6, 6, 6, 9, 7, 7, 5, 6, 6, 7, 7, 8, 7, 7, 7, 6, 8, 7, 9, 8, 7, 8, 9, 7, 8, 9, 8, 7, 7, 8, 8, 7, 9, 8, 9, 9, 9, 9, 9, 9, 8, 9, 10, 9, 10, 7, 9, 8, 9, 9, 9, 8, 9, 10, 9, 9, 10, 9, 10, 9, 9, 10, 10, 10, 9, 8, 9, 9, 10, 10, 10, 10, 10
Offset: 0
Examples
a(16) = 3 because 2^16 = 65536, which contains 3 distinct decimal digits [3,5,6].
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
Programs
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Maple
A043537 := proc(n) nops(convert(convert(n,base,10),set)) ; end: A137214 := proc(n) A043537(2^n) ; end: seq(A137214(n),n=0..120) ; # R. J. Mathar, Mar 16 2008 a:=proc(n) options operator, arrow: nops(convert(convert(2^n,base,10),set)) end proc: seq(a(n),n=0..80); # Emeric Deutsch, Apr 02 2008
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Mathematica
Table[Length[Union[IntegerDigits[2^n]]], {n, 0, 100}] (* T. D. Noe, Apr 01 2014 *) -
Python
def a(n): return len(set(str(2**n))) print([a(n) for n in range(99)]) # Michael S. Branicky, Jul 23 2021
Formula
a(n) = A043537(2^n). - R. J. Mathar, Mar 16 2008
Extensions
More terms from R. J. Mathar and Emeric Deutsch, Mar 16 2008
Comments