A134299 Maximal length of a sequence such that v(0)=n, v(k+2) = v(k)-v(k+1), v(k) >= 0.

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

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).

Links

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

Eric Angelini, Max Alekseyev and M. F. Hasler, Longest Lucas sequence from start to n, postings to Sequence Fans mailing list, Oct 18, 2007.

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