A173989 a(n) is the 2-adic valuation of A173300(n).

0, 0, 1, 1, 2, 1, 3, 3, 4, 3, 5, 5, 6, 5, 7, 7, 8, 7, 9, 9, 10, 9, 11, 11, 12, 11, 13, 13, 14, 13, 15, 15, 16, 15, 17, 17, 18, 17, 19, 19, 20, 19, 21, 21, 22, 21, 23, 23, 24, 23, 25, 25, 26, 25, 27, 27, 28, 27, 29, 29, 30, 29, 31, 31, 32, 31, 33, 33, 34, 33, 35, 35, 36, 35, 37, 37, 38, 37

Offset

1,5

Comments

Conjecture: always follows the pattern A, A, A+1, A, where A is an odd number.

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..1000

Formula

a(n) = log(A173300(n))/log(2).

Apparently a(n) = A102302(n) for n >= 7. - Hugo Pfoertner, Oct 10 2018

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: x^3*(1 + x^2 - x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.

(End)

Maple

From R. J. Mathar, Mar 20 2010: (Start)
A173300 := proc(n) local x, y ; x := (1+sqrt(3))/2 ; y := (1-sqrt(3))/2 ; denom(expand(x^n+y^n)) ; end proc:
A173989 := proc(n) log[2](A173300(n)) ; end proc: seq(A173989(n), n=3..100) ; (End)

Mathematica

Log2[Denominator[Map[First, NestList[{Last[#], Last[#] + First[#]/2} &, {1, 2}, 100]]]] (* Paolo Xausa, Feb 01 2024, after Nick Hobson in A173300 *)

Prog

(PARI) \\ using Max Alekseyev's function in A173300
A173300(n) = denominator(2*polcoeff( lift( Mod((1+x)/2, x^2-3)^n ), 0))
for(k=1, 74, print1(logint(A173300(k), 2), ", ")) \\ Hugo Pfoertner, Oct 10 2018

Crossrefs

Cf. A102302, A173300.

Sequence in context: A163281 A307857 A116921 * A093068 A097357 A342016

Adjacent sequences: A173986 A173987 A173988 * A173990 A173991 A173992

Keyword

nonn

Author

J. Lowell, Mar 04 2010

Extensions

More terms from R. J. Mathar and Max Alekseyev, Mar 20 2010

Status

approved