login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A134299 Maximal length of a sequence such that v(0)=n, v(k+2) = v(k)-v(k+1), v(k) >= 0. 1
4, 5, 6, 5, 7, 6, 5, 8, 6, 7, 6, 6, 9, 6, 7, 8, 6, 7, 6, 7, 10, 6, 7, 8, 7, 9, 6, 7, 8, 7, 7, 8, 7, 11, 7, 7, 8, 7, 9, 8, 7, 10, 7, 7, 8, 7, 9, 8, 7, 8, 7, 9, 8, 7, 12, 8, 7, 8, 7, 9, 8, 7, 10, 8, 9, 8, 7, 11, 8, 7, 8, 8, 9, 8, 7, 10, 8, 9, 8, 8, 9, 8, 7, 10, 8, 9, 8, 8, 13, 8, 9, 8, 8, 9, 8, 8, 10, 8, 9, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is also the maximal index at which n can occur in a Fibonacci-like sequence u(k+2) = u(k)+u(k+1) of nonnegative numbers.

A sequence of this length is obtained for v(0) = n, v(1) = A019446(n) = ceiling(n/tau) or A060143(n) = floor(n/tau).

REFERENCES

Eric Angelini, Max Alekseyev and M. F. Hasler, "Longest Lucas sequence from start to n", postings to Sequence Fans mailing list (seqfan(AT)ext.jussieu.fr), Oct 18, 2007

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

a(2007)=11 since there is no such sequence longer than v = (2007, 1240, 767, 473, 294, 179, 115, 64, 51, 13, 38).

PROG

(PARI) A134299( goal, mi=0, mx=0, new=0 ) = { for( j=mi, goal, a=[goal, new=j]; while( mi<=new=a[ #a-1]-new, a=concat(a, new)); if( #a>mx, mx=#a)); mx }

CROSSREFS

Cf. A101803, A019446, A060143.

Sequence in context: A113184 A136004 A248864 * A112780 A021223 A206291

Adjacent sequences:  A134296 A134297 A134298 * A134300 A134301 A134302

KEYWORD

nonn

AUTHOR

M. F. Hasler, Oct 18 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 18 12:13 EDT 2021. Contains 345098 sequences. (Running on oeis4.)