A183037 a(n) = A001511(n)*2^A001511(n) where A001511(n) equals the 2-adic valuation of 2n.

2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 384, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 896, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2, 8, 2, 160, 2, 8, 2, 24, 2, 8, 2, 64, 2, 8, 2, 24, 2

Offset

1,1

Comments

2n/2^A001511(n) is odd for n >= 1, so that A001511(n) is logarithmic in nature.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16383

Formula

Logarithmic derivative of A183036.

Example

L.g.f.: A(x) = 2*x + 8*x^2/2 + 2*x^3/3 + 24*x^4/4 + 2*x^5/5 + 8*x^6/6 + 2*x^7/7 + 64*x^8/8 + 2*x^9/9 + 8*x^10/10 + ...
The g.f. of A183036 begins:
exp(A(x)) = 1 + 2*x + 6*x^2 + 10*x^3 + 24*x^4 + 38*x^5 + 74*x^6 + ...

Mathematica

Array[# 2^# &[IntegerExponent[#, 2] + 1] &, 93] (* Michael De Vlieger, Nov 06 2018 *)

Prog

(PARI) {a(n)=valuation(2*n, 2)*2^valuation(2*n, 2)}
(Python)
def A183037(n): return (m:=n&-n)*m.bit_length()<<1 # Chai Wah Wu, Jul 12 2022

Crossrefs

Cf. A183036.

Sequence in context: A286455 A175183 A189217 * A063077 A245995 A085192

Adjacent sequences: A183034 A183035 A183036 * A183038 A183039 A183040

Keyword

nonn

Author

Paul D. Hanna, Dec 19 2010

Status

approved