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

0,6

Comments

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

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A180600 A006159 A376194 * A063273 A349481 A200262

Adjacent sequences: A081607 A081608 A081609 * A081611 A081612 A081613

Keyword

nonn,easy

Author

Reinhard Zumkeller, Mar 23 2003

Status

approved