The On-Line Encyclopedia of Integer Sequences (OEIS)

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A060901

Exact power of 3 that divides the n-th Fibonacci number (sequence A000045).
(history; published version)

#9 by Jon E. Schoenfield at Fri Mar 13 23:43:48 EDT 2015

STATUS

editing

approved

#8 by Jon E. Schoenfield at Fri Mar 13 23:43:46 EDT 2015

EXAMPLE

a(12) = 9 because the 12-th 12th Fibonacci number is 144 and 144 = 9*16.

STATUS

approved

editing

#7 by Reinhard Zumkeller at Wed Feb 04 13:20:22 EST 2015

STATUS

editing

approved

#6 by Reinhard Zumkeller at Wed Feb 04 13:16:17 EST 2015

PROG

(Haskell)

a060901 = a038500 . a000045 -- Reinhard Zumkeller, Feb 04 2015

CROSSREFS

Cf. A038500.

#5 by Reinhard Zumkeller at Wed Feb 04 13:14:47 EST 2015

LINKS

Reinhard Zumkeller, <a href="/A060901/b060901.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#4 by Bruno Berselli at Tue Jul 30 11:44:28 EDT 2013

STATUS

proposed

approved

#3 by Michel Marcus at Tue Jul 30 11:24:32 EDT 2013

STATUS

editing

proposed

#2 by Michel Marcus at Tue Jul 30 11:23:57 EDT 2013

FORMULA

If n is not divisible by 4 then a(n) = 1, if n = 4 * 3^k * m where m is not divisible by 3 then a(n) = 3^(k+1).

a(n) = A038500(A000045(n)). - Michel Marcus, Jul 30 2013

EXAMPLE

a(12) = 9 because the 12-th Fibonacci number is 144 and 144 = 9*16.

PROG

(PARI) a(n) = 3^valuation(fibonacci(n), 3) \\Michel Marcus, Jul 30 2013

CROSSREFS

Cf. A000045, A060865.

STATUS

approved

editing

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Exact power of 3 that divides the n-th Fibonacci number (sequence A000045).

DATA

1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 27, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 27, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 9, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1

OFFSET

1,4

FORMULA

If n is not divisible by 4 then a(n) = 1, if n = 4 * 3^k * m where m is not divisible by 3 then a(n) = 3^(k+1)

EXAMPLE

a(12) = 9 because the 12-th Fibonacci number is 144 and 144 = 9*16

CROSSREFS

A000045, A060865.

KEYWORD

nonn,easy

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), May 05 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), May 07 2001

STATUS

approved