A327492 Partial sums of A327491.

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, 48, 49, 51, 53, 55, 56, 58, 63, 65, 66, 68, 70, 72, 73, 75, 78, 80, 81, 83, 85, 87, 88, 90, 94, 96, 97, 99, 101, 103, 104, 106, 109, 111, 112, 114, 116, 118, 119

Offset: 0

Author

Peter Luschny, Sep 27 2019

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A327491, A005187, A327493, A327494, A327495.

Programs

Julia

bitcount(n) = sum(digits(n, base = 2))
A327492(n) = 2n - bitcount(n) + mod(n, 2)
[A327492(n) for n in 0:62] |> println # Peter Luschny, Oct 03 2019

Maple

# For len >= 1:
A327492_list := len -> ListTools:-PartialSums([seq(A327491(j), j=0..len-1)]):
A327492_list(99)

Mathematica

a[n_] := 2*n + Mod[n, 2] - DigitCount[2*n, 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Aug 30 2024 *)

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

PARI

a(n) = n<<1 - hammingweight(n) + bittest(n,0); \\ Kevin Ryde, May 31 2022

SageMath

@cached_function
def A327492(n):
    if n == 0: return 0
    r = valuation(n, 2) if 4.divides(n) else n % 2 + 1
    return r + A327492(n-1)
print([A327492(n) for n in (0..19)])

Formula

a(n) = A005187(n) + n mod 2.

a(n) ~ 2*n. - Amiram Eldar, Aug 30 2024