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%I #43 Apr 09 2018 12:23:27
%S 1,3,3,1,3,3,3,4,1,4,3,3,3,5,4,1,3,3,3,3,3,3,3,3,1,4,5,4,3,3,3,3,5,4,
%T 4,1,3,3,3,3,3,3,3,3,3,3,3,3,1,3,5,6,3,4,5,3,3,4,3,5,3,4,5,1,6,5,3,3,
%U 3,5,3,5,3,3,6,3,4,5,3,3,1,3,3,4,5,3,3,3,3,6,6,5,3,3,5,3,3,6,7,1,3,6,3,5,4
%N Smallest values of t arising in R. L. Graham's sequence (A006255).
%C Length of n-th row in table A245499. - _Reinhard Zumkeller_, Jul 25 2014
%C Indices of records are 1, 2, 8, 14, 52, 99, 589, 594, 595... (A277649) - _Peter Kagey_, Oct 24 2016
%C It is conjectured that 2 never appears in this sequence. a(n) = 2 if and only if A006255(n) = A072905(n). - _Peter Kagey_, Oct 25 2016
%C a(n) is three most of the time, then 5, then 6, then 4 for the first 1000 and the first 10000 terms. At n = 72, 78 and 85, a(n) is 4 or 5 and 4 and 5 occured equally often so far. At 299, 301, 312, 322 and 403, a(n) is 4 or 6 and 4 and 6 occured equally often so far. This doesn't happen for the first 10000 terms for 5 and 6. - _David A. Corneth_, Oct 25 2016
%D R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 147.
%H David A. Corneth, <a href="/A066400/b066400.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Reinhard Zumkeller and Peter Kagey)
%H R. L. Graham, <a href="http://www.jstor.org/stable/2689569">Bijection between integers and composites</a>, Problem 1242, Math. Mag., 60 (1987), p. 180.
%e a(2) = 3 because the best such sequence is 2,3,6 which has three terms.
%o (Haskell)
%o a066400 = length . a245499_row -- _Reinhard Zumkeller_, Jul 25 2014
%Y Cf. A006255, A066401.
%Y Cf. A245499, A277649.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Dec 25 2001
%E More terms from _John W. Layman_, Jul 14 2003
%E More terms from _Joshua Zucker_, May 18 2006
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