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%I #42 Jan 02 2023 12:30:46
%S 1,2,3,4,6,9,10,12,18,33,34,36,40,64,66,192,256,264,272,513,514,516,
%T 576,768,1026,1056,2304,16392,65664,81920,532480,545259520
%N Neither 4 nor 9 divides C(2n-1,n) (almost certainly finite).
%C Complete up to 2^64 = 18446744073709551616.
%C Complete up to 2^30000. - _Don Reble_, Oct 27 2013
%C 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
%C 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
%D A.-M. Legendre, Théorie de Nombres, Firmin Didot Frères, Paris, 1830.
%H E. E. Kummer, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002147432">Uber die Ergänzungssätze zu den allgemeinen Reciprocitätsgesetzen</a>, J. Reine Angew Math. 44 (1852), 93-146.
%H Don Reble, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-October/011806.html">A051404</a>, SeqFan Post, Oct 30 2013
%H V. Shevelev, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Shevelev/shevelev14.html">Binomial coefficient predictors</a>, J. of integer sequences, Vol. 14 (2011), Article 11.2.8.
%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-October/011817.html">Re: A051404</a>, SeqFan Post, Oct 30 2013
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Kummer's_theorem">Kummer's Theorem</a>
%e 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
%K nonn
%O 1,2
%A _David W. Wilson_
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