A346502 a(n) = 3n - (sum of digits of 3n in base 3).

0, 2, 4, 8, 10, 12, 16, 18, 20, 26, 28, 30, 34, 36, 38, 42, 44, 46, 52, 54, 56, 60, 62, 64, 68, 70, 72, 80, 82, 84, 88, 90, 92, 96, 98, 100, 106, 108, 110, 114, 116, 118, 122, 124, 126, 132, 134, 136, 140, 142, 144, 148, 150, 152, 160, 162, 164, 168, 170, 172

Offset: 0

Author

Bernard Schott, Jul 21 2021

Keywords

• nonn
• base

Comments

Terms of A344853 without repetition.

All terms are even.

A new largest gap between 2 consecutive terms is obtained between a(3^m-1) and a(3^m), m >= 0 (see formula).

In base 2, A005187(n) = 2n - (sum of digits of 2n in base 2) is also the exponent of the largest power of 2 dividing (2n)!, but here the exponent of the largest power of 3 dividing (3n)! is not a(n) but A004128(n).

Examples

			a(8) = 24 - (sum of digits of 24 in base 3); 24_10 = 220_3 and 2+2+0 = 4, so a(8) = 24-4 = 20.
		

Crossrefs

Cf. A005187 (similar, with base 2).

Cf. A004128, A053735, A344853.

Programs

Mathematica

a[n_] := 3*n - Plus @@ IntegerDigits[3*n, 3]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2021 *)

PARI

a(n) = 3*n - sumdigits(n,3); \\ Kevin Ryde, Jul 21 2021

Python

from sympy.ntheory.digits import digits
def a(n): return 3*n - sum(digits(3*n, 3)[1:])
print([a(n) for n in range(60)]) # Michael S. Branicky, Jul 28 2021

Formula

a(n) = 3*n - A053735(3*n).

a(n) = 2*A004128(n).

a(n) = A344853(3n).

a(3^n) - a(3^n-1) = 2*(n+1).