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A327492 Partial sums of A327491.

%I A327492 #22 Aug 30 2024 06:25:28
%S A327492 0,2,3,5,7,9,10,12,15,17,18,20,22,24,25,27,31,33,34,36,38,40,41,43,46,
%T A327492 48,49,51,53,55,56,58,63,65,66,68,70,72,73,75,78,80,81,83,85,87,88,90,
%U A327492 94,96,97,99,101,103,104,106,109,111,112,114,116,118,119
%N A327492 Partial sums of A327491.
%H A327492 Amiram Eldar, <a href="/A327492/b327492.txt">Table of n, a(n) for n = 0..10000</a>
%F A327492 a(n) = A005187(n) + n mod 2.
%F A327492 a(n) ~ 2*n. - _Amiram Eldar_, Aug 30 2024
%p A327492 # For len >= 1:
%p A327492 A327492_list := len -> ListTools:-PartialSums([seq(A327491(j), j=0..len-1)]):
%p A327492 A327492_list(99)
%t A327492 a[n_] := 2*n + Mod[n, 2] - DigitCount[2*n, 2, 1]; Array[a, 100, 0] (* _Amiram Eldar_, Aug 30 2024 *)
%o A327492 (SageMath)
%o A327492 @cached_function
%o A327492 def A327492(n):
%o A327492     if n == 0: return 0
%o A327492     r = valuation(n, 2) if 4.divides(n) else n % 2 + 1
%o A327492     return r + A327492(n-1)
%o A327492 print([A327492(n) for n in (0..19)])
%o A327492 (PARI) seq(n)={my(a=vector(n+1)); for(n=1, n, a[n+1] = a[n] + if(n%4, n%2 + 1, valuation(n,2))); a} \\ _Andrew Howroyd_, Sep 28 2019
%o A327492 (PARI) a(n) = n<<1 - hammingweight(n) + bittest(n,0); \\ _Kevin Ryde_, May 31 2022
%o A327492 (Julia)
%o A327492 bitcount(n) = sum(digits(n, base = 2))
%o A327492 A327492(n) = 2n - bitcount(n) + mod(n, 2)
%o A327492 [A327492(n) for n in 0:62] |> println # _Peter Luschny_, Oct 03 2019
%Y A327492 Cf. A327491, A005187, A327493, A327494, A327495.
%K A327492 nonn,easy
%O A327492 0,2
%A A327492 _Peter Luschny_, Sep 27 2019