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A183037
a(n) = A001511(n)*2^A001511(n) where A001511(n) equals the 2-adic valuation of 2n.
3
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 19 2010
STATUS
approved