A081610 Number of numbers <= n having at least one 2 in their ternary representation.

0, 0, 1, 1, 1, 2, 3, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 19, 20, 20, 20, 21, 22, 23, 24, 24, 24, 25, 25, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53

Offset: 0

Author

Reinhard Zumkeller, Mar 23 2003

Keywords

• nonn
• easy

Comments

a(n) + A081611(n) = n+1. Partial sums of A189820.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A007089, A081603, A081607, A081609, A189820.

Programs

Maple

num2tern := proc(n) return numboccur(convert(n,base,3),2): end: a:=0: for n from 0 to 80 do a:=a+`if`(num2tern(n)>0,1,0): printf("%d, ",a): od: # Nathaniel Johnston, May 17 2011

Mathematica

Accumulate[Table[If[DigitCount[n,3,2]>0,1,0],{n,0,70}]] (* Harvey P. Dale, Aug 20 2012 *)

PARI

first(n)=my(s,t); vector(n,k,t=Set(digits(k,3)); s+=t[#t]==2) \\ Charles R Greathouse IV, Sep 02 2015

Python

from gmpy2 import digits
def A081610(n):
    l = (s:=digits(n,3)).find('2')
    if l >= 0: s = s[:l]+'1'*(len(s)-l)
    return n-int(s,2) # Chai Wah Wu, Dec 05 2024

Formula

a(n) ~ n. - Charles R Greathouse IV, Sep 02 2015