A324468 a(n) = r(n) + r(n+1) + r(n+2), where r(n) is the ruler sequence A007814.

1, 3, 2, 3, 1, 4, 3, 4, 1, 3, 2, 3, 1, 5, 4, 5, 1, 3, 2, 3, 1, 4, 3, 4, 1, 3, 2, 3, 1, 6, 5, 6, 1, 3, 2, 3, 1, 4, 3, 4, 1, 3, 2, 3, 1, 5, 4, 5, 1, 3, 2, 3, 1, 4, 3, 4, 1, 3, 2, 3, 1, 7, 6, 7, 1, 3, 2, 3, 1, 4, 3, 4, 1, 3, 2, 3, 1, 5, 4, 5, 1, 3, 2, 3, 1

Offset: 1

Author

N. J. A. Sloane, Mar 03 2019

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001511, A007814, A050603 (r(n)+r(n+1)), A324465.

Programs

Magma

[&+[Valuation(n+k, 2): k in [0..2]]: n in [1..70]]; // Vincenzo Librandi, Mar 10 2019

Mathematica

Table[Sum[IntegerExponent[n + k, 2], {k, 0, 2}], {n, 100}] (* Vincenzo Librandi, Mar 10 2019 *)

PARI

a(n) = sum(k=0, 2, valuation(n+k, 2)); \\ Michel Marcus, Mar 10 2019

Python

def A324468(n): return (~n & n-1).bit_length()+(~(n+1) & n).bit_length()+(~(n+2) & n+1).bit_length() # Chai Wah Wu, Jul 01 2022

Formula

1 <= a(n) <= 1 + log_2(n+2). - Charles R Greathouse IV, Jul 01 2022

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3. - Amiram Eldar, Sep 10 2024