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A090739 Exponent of 2 in 9^n - 1. 12
3, 4, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 4, 3, 7, 3, 4, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 4, 3, 8, 3, 4, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 4, 3, 7, 3, 4, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 4, 3, 9, 3, 4, 3, 5, 3, 4, 3, 6, 3, 4, 3, 5, 3, 4, 3, 7, 3, 4, 3, 5, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The exponent of 2 in the factorization of Fibonacci(6n). - T. D. Noe, Mar 14 2014

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

T. Lengyel, The order of the Fibonacci and Lucas numbers, Fib. Quart. 33 (1995), 234-239.

FORMULA

a(n) = A007814(n) + 3.

a((2*n-1)*2^p) = p + 3, p >= 0. - Johannes W. Meijer, Feb 08 2013

a(n) = log_2(A006519(9^n - 1)). - Alonso del Arte, Feb 08 2013

EXAMPLE

For n = 2, we see that -1 + 3^4 = 80 = 2^4 * 5 so a(2) = 4.

For n = 3, we see that -1 + 3^6 = 728 = 2^3 * 7 * 13, so a(3) = 3.

MAPLE

nmax:=70: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := p+3: od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Feb 08 2013

MATHEMATICA

Table[Part[Flatten[FactorInteger[ -1+3^(2*n)]], 2], {n, 1, 70}]

Table[IntegerExponent[Fibonacci[n], 2], {n, 6, 600, 6}] (* T. D. Noe, Mar 14 2014 *)

PROG

(PARI) a(n)=valuation(n, 2)+3 \\ Charles R Greathouse IV, Mar 14 2014

CROSSREFS

Cf. A024101, A069895, A091512, A088660, A090740, A220466.

Appears in A161737.

Sequence in context: A223169 A201420 A244055 * A076400 A121889 A205692

Adjacent sequences:  A090736 A090737 A090738 * A090740 A090741 A090742

KEYWORD

nonn,easy

AUTHOR

Labos Elemer and Ralf Stephan, Jan 19 2004

EXTENSIONS

More terms from T. D. Noe, Mar 14 2014

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)