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A051404 Neither 4 nor 9 divides C(2n-1,n) (almost certainly finite). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A175515

Adjacent sequences:  A051401 A051402 A051403 * A051405 A051406 A051407

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)