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

0,2

Links

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

Formula

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

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

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 *)

Prog

(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)])
(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
(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

Crossrefs

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

Sequence in context: A083033 A022847 A047371 * A044918 A103635 A133677

Adjacent sequences: A327489 A327490 A327491 * A327493 A327494 A327495

Keyword

nonn,easy

Author

Peter Luschny, Sep 27 2019

Status

approved