

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
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OFFSET

1,1


COMMENTS

This is also the maximal index at which n can occur in a Fibonaccilike 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[ #a1]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



