A324468 - OEIS

%I #20 Sep 10 2024 08:44:15

%S 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,

%T 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,

%U 1,4,3,4,1,3,2,3,1,5,4,5,1,3,2,3,1

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

%H Vincenzo Librandi, <a href="/A324468/b324468.txt">Table of n, a(n) for n = 1..10000</a>

%F 1 <= a(n) <= 1 + log_2(n+2). - _Charles R Greathouse IV_, Jul 01 2022

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

%t Table[Sum[IntegerExponent[n + k, 2], {k, 0, 2}], {n, 100}] (* _Vincenzo Librandi_, Mar 10 2019 *)

%o (Magma) [&+[Valuation(n+k, 2): k in [0..2]]: n in [1..70]]; // _Vincenzo Librandi_, Mar 10 2019

%o (PARI) a(n) = sum(k=0, 2, valuation(n+k, 2)); \\ _Michel Marcus_, Mar 10 2019

%o (Python)

%o 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

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

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Mar 03 2019