A238462 2-adic valuation of A052129.

0, 0, 1, 2, 6, 12, 25, 50, 103, 206, 413, 826, 1654, 3308, 6617, 13234, 26472, 52944, 105889, 211778, 423558, 847116, 1694233, 3388466, 6776935, 13553870, 27107741, 54215482, 108430966, 216861932, 433723865, 867447730

Offset

0,4

Links

Kenny Lau, Table of n, a(n) for n = 0..3323

Formula

From Ridouane Oudra, Sep 03 2019: (Start)

a(n) = Sum_{i=1..n} 2^(n-i)*v_2(i), where v_2(i) = A007814(i).

More generally, the p-adic valuation of A052129 for any prime p is given by

v_p(A052129(n)) = Sum_{i=1..n} 2^(n-i)*v_p(i), where v_p(i) is the exponent of the highest power of p dividing i. (End)

Maple

with(padic): seq(add(2^(n-i)*ordp(i, 2), i=1..n), n=0..60); # Ridouane Oudra, Sep 03 2019

Mathematica

Map[IntegerExponent[#, 2] &, Nest[Append[#, Length[#]*#[[-1]]^2] &, {1}, 31]] (* or, per first formula, more efficiently, *)
Array[Sum[2^(# - i)*IntegerExponent[i, 2], {i, #}] &, 32, 0] (* Michael De Vlieger, Sep 29 2019 *)

Prog

(PARI)
A052129(n) = if( n<1, n==0, prod(k=0, n-1, (n - k)^2^k));
a(n) = valuation(A052129(n), 2);
(PARI) a(n) = fromdigits(vector(n, i, valuation(i, 2)), 2); \\ Kevin Ryde, Oct 08 2021
(Python)
n=4000; val=[0]*(n+1); exp=2
while exp <= n:
    for j in range(exp, n+1, exp): val[j] += 1
    exp *= 2
res = 0; i = 0
while len(str(res)) <= 1000: print(i, res); i += 1; res = res * 2 + val[i]
# Kenny Lau, Jun 09 2018

Crossrefs

Sequence in context: A045925 A128020 A140659 * A099495 A232164 A214663

Adjacent sequences: A238459 A238460 A238461 * A238463 A238464 A238465

Keyword

nonn

Author

Joerg Arndt, Feb 27 2014

Extensions

Incorrect comment removed by Michel Marcus, Oct 06 2019

Status

approved