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

Author

Reinhard Zumkeller, May 20 2005

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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 *)

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

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)).

Extensions

Corrected by T. D. Noe, Oct 25 2006

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