Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A129066
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A129066 Numbers n such that n divides Fibonacci(n) with multiples of 12 excluded. +0
1
1, 5, 25, 125, 625, 3125, 15625, 75025, 78125, 375125, 390625, 1875625, 1953125, 9378125, 9765625, 46890625, 48828125 (list; graph; listen)
OFFSET

1,2

COMMENT

a(n) includes all terms of A023172(n) with terms 12*A072378(n) excluded.

No other terms below 10^8.

Since 5*F(m) divides F(5*m), if m is in this sequence then 5*m is. Also, if m is in this sequence (i.e., gcd(F(m),m)=m) then F(m) is in this sequence (since gcd(F(F(m)),F(m)) = F(gcd(F(m),m)) = F(m)).

In particular, a(n) includes all terms of geometric progressions 5^k*Fibonacci(5^m) for integers k>=0 and m>=0.

Open question: does a(n) include the powers of Fibonacci(5^k) and the terms of the form Fibonacci(5^k)*Fibonacci(5^m); or is it closed under multiplication?

EXAMPLE

a(1) = Fibonacci(5) = 5, a(2)-a(6) = {5^2, 5^3, 5^4, 5^5, 5^6}, a(7) = 75025 = 5^2*3001 = Fibonacci(5^2), a(8) = 5^7, a(9) = 375125 = 5^3*3001 = 5*Fibonacci(5^2), a(10) = 5^8.

MATHEMATICA

Do[ If[ !IntegerQ[ n/12 ] && IntegerQ[ Fibonacci[n] / n ], Print[n] ], {n, 1, 5^8} ]

CROSSREFS

Cf. A072378, A023172.

Sequence in context: A057831 A014946 A132839 this_sequence A102169 A060391 A000351

Adjacent sequences: A129063 A129064 A129065 this_sequence A129067 A129068 A129069

KEYWORD

hard,more,nonn,new

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), May 11 2007

EXTENSIONS

Edited and extended by Max Alekseyev (maxale(AT)gmail.com), Sep 20 2009

a(1)=1 added by Zak Seidov (zakseidov(AT)yahoo.com), Nov 01 2009

page 1

Search completed in 0.003 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


AT&T Labs Research