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A134299
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Maximal length of a sequence such that v(0)=n, v(k+2) = v(k)-v(k+1), v(k) >= 0.
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1
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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; internal format)
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OFFSET
| 1,1
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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) = ceil(n/tau) or A060143(n) = floor(n/tau).
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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
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EXAMPLE
| a(2007)=11 since there is no such sequence longer than v = (2007, 1240, 767, 473, 294, 179, 115, 64, 51, 13, 38)
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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 }
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CROSSREFS
| Cf. A101803, A019446, A060143.
Sequence in context: A002129 A113184 A136004 * A112780 A021223 A058979
Adjacent sequences: A134296 A134297 A134298 * A134300 A134301 A134302
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KEYWORD
| nonn
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AUTHOR
| M. F. Hasler (maximilian.hasler(AT)gmail.com), Oct 18 2007
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