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

Author

Ctibor O. Zizka, Mar 06 2008

Keywords

• easy
• nonn
• base

Comments

Appears to be all 10's starting at a(169). - T. D. Noe, Apr 01 2014

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

Crossrefs

Cf. A043562, A043536.

Programs

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

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