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

1,2

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 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

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.

Example

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

Prog

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

Crossrefs

Cf. A006255, A066401.

Cf. A245499, A277649.

Sequence in context: A171369 A111629 A083953 * A125562 A337910 A092040

Adjacent sequences: A066397 A066398 A066399 * A066401 A066402 A066403

Keyword

nonn

Author

N. J. A. Sloane, Dec 25 2001

Extensions

More terms from John W. Layman, Jul 14 2003

More terms from Joshua Zucker, May 18 2006

Status

approved