A324465 Exponent of highest power of 2 that divides A324152(n).

0, 0, 1, 3, 2, 2, 3, 5, 2, 3, 4, 6, 5, 4, 5, 7, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 6, 7, 9, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 7, 8, 10, 5, 6, 7, 9, 8, 8, 9, 11, 8, 9, 10, 12, 11, 8, 9, 11, 2, 3, 4, 6, 5, 5, 6, 8, 5, 6, 7, 9, 8, 7, 8, 10, 5, 6, 7, 9

Offset

0,4

Comments

First occurrence of k=0,1,2,...: 0, 2, 4, 3, 10, 7, 11, 15, 23, 27, 47, 55, 59, 111, 119, 123, 239, 247, 251, 495, 503, 507, 1007, 1015, 1019, 2031, 2039, 2043, 4079, 4087, 4091, 8175, 8183, 8187, 16367, 16375, 16379, 32751, 32759, 32763, 65519, 65527, 65531, 131055, 131063, 131067, ..., . Robert G. Wilson v, Mar 01 2019

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (first 501 terms from N. J. A. Sloane)

Formula

a(n) = 3*wt(n) - (2-adic valuation of (n+1)*(n+2)*(n+3))

= 3*A000120(n) - (A007814(n+1)+A007814(n+2)+A007814(n+3)).

E.g. if n = 14 = 1110_2, with weight 3, we get a(14) = 3*3 - 2-adic valuation of 15*16*17 = 9 - 4 = 5.

Mathematica

f[n_] := IntegerExponent[(3/((n + 1)(n + 2)(n + 3)))*Multinomial[n, n, n, n], 2]; f[0] = 0; Array[f, 84, 0] (* Robert G. Wilson v, Mar 01 2019 *)

Prog

(Python 3.10+)
def A324465(n): return 3*n.bit_count()-(~(n+1)&n).bit_length()-(~(n+2)&n+1).bit_length()-(~(n+3)&n+2).bit_length() if n else 0 # Chai Wah Wu, Jul 10 2022
(PARI) a(n) = 3*hammingweight(n) - valuation((n+1)*(n+2)*(n+3), 2); \\ Michel Marcus, Jul 10 2022

Crossrefs

Cf. A000120 (binary weight), A007814, A324152, A324467.

Sequence in context: A222673 A222666 A335401 * A361565 A334592 A248756

Adjacent sequences: A324462 A324463 A324464 * A324466 A324467 A324468

Keyword

nonn

Author

N. J. A. Sloane, Mar 01 2019

Status

approved