A107680 Repeating k-th ternary repunit (A003462) 2^k times, k >= 0.

0, 1, 1, 4, 4, 4, 4, 13, 13, 13, 13, 13, 13, 13, 13, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121, 121

Offset

0,4

Comments

a(n) is the greatest ternary repunit that is not greater than the n-th number with no 2 in ternary representation.

Links

Table of n, a(n) for n=0..61.

Formula

A032924(n) = a(n) + A107681(n);

A081604(A107681(n)) <= A081604(a(n)) = A081604(A032924(n)) = A000523(n+1).

a(n) = A003462(A000523(n+1)).

Example

k=1: A003462(1) = (3^1-1)/2 = 1, therefore a(1) = a(2^1) = 1;
k=2: A003462(2) = (3^2-1)/2 = 4, therefore a(2+1) = a(2+2) =
a(2+3) = a(2+2^2) = 4.

Mathematica

With[{nn=5}, Flatten[Table[#[[1]], {#[[2]]}]&/@Thread[{Table[FromDigits[ PadRight[{}, n, 1], 3], {n, nn}], 2^Range[nn]}]]] (* Harvey P. Dale, Jan 04 2013 *)

Prog

(PARI) apply( {A107680(n)=3^exponent(n+1)\2}, [0..66]) \\ M. F. Hasler, Jun 22 2020
(Python)
def A107680(n): return 3**((n+1).bit_length()-1)-1>>1 # Chai Wah Wu, Nov 07 2024

Crossrefs

Cf. A007089, A003462 (repunits in base 3), A000523 (number of digits in binary representation of n).

Sequence in context: A046109 A377748 A294246 * A358509 A285052 A369719

Adjacent sequences: A107677 A107678 A107679 * A107681 A107682 A107683

Keyword

nonn

Author

Reinhard Zumkeller, May 20 2005

Extensions

Corrected by T. D. Noe, Oct 25 2006

Extended to a(0) = 0 by M. F. Hasler, Jun 23 2020

Status

approved