A328034 a(n) = 3n minus the largest power of 2 not exceeding 3n.

1, 2, 1, 4, 7, 2, 5, 8, 11, 14, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109

Offset

1,2

Comments

For odd n, a(n) is odd. For even n, a(n) = 2*a(n/2).

Conjecture: iterations of a() stabilize at a power of 2, or at a 2-cycle (5*2^t,7*2^t).

Links

Table of n, a(n) for n=1..79.

Max Alekseyev, Proof that representation 3^n s - \sum_{k=0}^{n-1} 3^{n-k-1} 2^{a_k} = 2^m exists for any s. MathOverflow, 2019.

Formula

a(n) = A053645(3*n).

Prog

(PARI) { A328034(n) = 3*n - 1<<(log(3*n+.5)\log(2)); }

Crossrefs

Sequence in context: A030102 A072010 A255588 * A123360 A072015 A123242

Adjacent sequences: A328031 A328032 A328033 * A328035 A328036 A328037

Keyword

nonn

Author

Max Alekseyev, Nov 10 2019

Status

approved