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

0,2

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).

Links

Table of n, a(n) for n=0..59.

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).

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A005187 (similar, with base 2).

Cf. A004128, A053735, A344853.

Sequence in context: A195066 A036990 A097498 * A321580 A224694 A140900

Adjacent sequences: A346499 A346500 A346501 * A346503 A346504 A346505

Keyword

nonn,base

Author

Bernard Schott, Jul 21 2021

Status

approved