A309432 Number of distinct digits in decimal representation of n^2.

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 2, 3, 4, 4, 3, 3, 4, 4, 2, 3, 3, 3, 4, 4, 4, 3, 3, 3, 4, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 3, 4, 3, 3, 4, 3, 4, 4, 4, 4, 3, 3, 3, 4, 4, 3, 3, 4, 3, 4, 3, 4

Offset: 0

Author

Hauke Löffler, Aug 01 2019

Keywords

• nonn
• base
• easy

Examples

			a(0) = 1 because 0^2 = 0 has 1 distinct digit (0).
a(5) = 2 because 5^2 = 25 has 2 distinct digits (2, 5).
a(10) = 2 because 10^2 = 100 has 2 distinct digits (0, 1).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290 (squares), A043537, A054039, A137214, A185679, A309431.

Programs

Mathematica

Array[Count[DigitCount[#^2], ?(# > 0 &)] &, 105, 0] (* _Michael De Vlieger, Jun 22 2022 *)

PARI

a(n) = if(n==0, 1, #Set(digits(n^2))); \\ Jinyuan Wang, Aug 02 2019, Jun 22 2022 [a(0)=1 corrected by Georg Fischer, Jun 22 2022]

Python

def a(n): return len(set(str(n*n)))
print([a(n) for n in range(87)]) # Michael S. Branicky, Jun 22 2022

SageMath

[len(set(Integer((n^2)).digits(padto=1))) for n in range(25) ]