A051404 Neither 4 nor 9 divides C(2n-1,n) (almost certainly finite).

1, 2, 3, 4, 6, 9, 10, 12, 18, 33, 34, 36, 40, 64, 66, 192, 256, 264, 272, 513, 514, 516, 576, 768, 1026, 1056, 2304, 16392, 65664, 81920, 532480, 545259520

Offset

1,2

Comments

Complete up to 2^64 = 18446744073709551616.

Complete up to 2^30000. - Don Reble, Oct 27 2013

A number n is in the sequence if and only if the following inequalities hold s_2(n) <= 2 and s_3(n) + s_3(n-1) - s_3(2*n-1) <= 2, where s_m(n) is sum of digits of n in base m. - Vladimir Shevelev, Oct 30 2013

Equivalently, a number n is in the sequence if and only if there is at most 1 "carry" when adding n and n-1 in both base-2 arithmetic and base-3 arithmetic. - Tom Edgar, Oct 31 2013

References

A.-M. Legendre, Théorie de Nombres, Firmin Didot Frères, Paris, 1830.

Links

Table of n, a(n) for n=1..32.

E. E. Kummer, Uber die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen, J. Reine Angew Math. 44 (1852), 93-146.

Don Reble, A051404, SeqFan Post, Oct 30 2013

V. Shevelev, Binomial coefficient predictors, J. of integer sequences, Vol. 14 (2011), Article 11.2.8.

Vladimir Shevelev, Re: A051404, SeqFan Post, Oct 30 2013

Wikipedia, Kummer's Theorem

Example

For n=64 we have s_2(64)=1, s_3(n)=4, s_3(64-1)=3, s_3(2*64-1)=5 and 4+3-5=2. So 64 is in the sequence. - Vladimir Shevelev, Oct 30 2013

Crossrefs

Sequence in context: A014851 A177919 A128399 * A046097 A239580 A337724

Adjacent sequences: A051401 A051402 A051403 * A051405 A051406 A051407

Keyword

nonn

Author

David W. Wilson

Status

approved