A066400 Smallest values of t arising in R. L. Graham's sequence (A006255).

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Dec 25 2001

Keywords

• nonn

Comments

Length of n-th row in table A245499. - Reinhard Zumkeller, Jul 25 2014

Indices of records are 1, 2, 8, 14, 52, 99, 589, 594, 595... (A277649) - Peter Kagey, Oct 24 2016

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

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 occurred equally often so far. At 299, 301, 312, 322 and 403, a(n) is 4 or 6 and 4 and 6 occurred equally often so far. This doesn't happen for the first 10000 terms for 5 and 6. - David A. Corneth, Oct 25 2016

Examples

			a(2) = 3 because the best such sequence is 2,3,6 which has three terms.
		

References

• R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 147.

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from Reinhard Zumkeller and Peter Kagey)
• R. L. Graham, Bijection between integers and composites, Problem 1242, Math. Mag., 60 (1987), p. 180.

Crossrefs

Cf. A006255, A066401, A072905.

Cf. A245499, A277649.

Programs

Haskell

a066400 = length . a245499_row  -- Reinhard Zumkeller, Jul 25 2014

Extensions

More terms from John W. Layman, Jul 14 2003

More terms from Joshua Zucker, May 18 2006