A107681 Repeat(first 2^k numbers with no 2 in ternary representation) for k>0.

0, 1, 0, 1, 3, 4, 0, 1, 3, 4, 9, 10, 12, 13, 0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37, 39, 40, 81, 82, 84, 85, 90, 91, 93, 94, 108, 109, 111, 112, 117, 118, 120, 121, 0, 1, 3, 4, 9, 10, 12, 13, 27, 28, 30, 31, 36, 37

Offset

1,5

Comments

let A032924(n) = Sum(d(i)*3^i: 0<d(i)<3, 0<=i<L)

then .... a(n) = Sum((d(i)-1)*3^i: 0<=i<L);

A032924(n) = A107680(n) + a(n);

A081604 (a(n)) <= A081604(A107680(n)) = A081604(A032924(n)) = A000523(n+1).

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..8190 (12 rows).

Formula

a(n) = A005836(A062050(n+1)).

Example

A032924(177) = A107680(177) + a(177),
....... 1420 = ....... 1093 + 327,
.. '1221121' = ... '1111111'+ '110010',
............ = . A003462(7) + A005836(51).

Prog

(PARI) a(n)= fromdigits(binary(n+1-1<<logint(n+1, 2)), 3); \\ Ruud H.G. van Tol, Nov 18 2024
(Python)
def A107681(n): return int(bin(n+1)[3:], 3) # Chai Wah Wu, May 06 2025

Crossrefs

Cf. A000523, A005836, A003462, A007089, A032924, A062050, A081604, A107680.

Sequence in context: A016653 A381348 A096088 * A021298 A170952 A194587

Adjacent sequences: A107678 A107679 A107680 * A107682 A107683 A107684

Keyword

nonn,easy,look

Author

Reinhard Zumkeller, May 20 2005

Extensions

Data corrected by Ruud H.G. van Tol, Nov 18 2024.

Status

approved