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Search: id:A107757
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| A107757 |
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Numbers n such that Sum_{k=1..n} Catalan(k) == 2 mod 3. |
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+0
4
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| 3, 9, 11, 27, 29, 35, 39, 81, 83, 89, 93, 107, 111, 117, 119, 243, 245, 251, 255, 269, 273, 279, 281, 323, 327, 333, 335, 351, 353, 359, 363, 729, 731, 737, 741, 755, 759, 765, 767, 809, 813, 819, 821, 837, 839, 845, 849, 971, 975, 981, 983, 999, 1001, 1007, 1011
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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Y. More, Problem 11165, Amer. Math. Monthly, 112 (2005), 568.
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MAPLE
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c:=n->binomial(2*n, n)/(n+1): s:=0: for n from 1 to 1500 do s:=s+c(n): a[n]:=s mod 3: od: A:=[seq(a[n], n=1..1500)]: p:=proc(n) if A[n]=2 then n else fi end: seq(p(n), n=1..1500); (Deutsch)
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MATHEMATICA
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s0 = s2 = {}; s = 0; Do[s = Mod[s + (2 n)!/n!/(n + 1)!, 3]; Switch[ Mod[s, 3], 0, AppendTo[s0, n], 2, AppendTo[s2, n]], {n, 1055}]; s2 (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 14 2005
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CROSSREFS
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Cf. A000108, A107755, A107756.
Equals A074939 - 1.
Sequence in context: A032915 A019080 A060141 this_sequence A057261 A003597 A018705
Adjacent sequences: A107754 A107755 A107756 this_sequence A107758 A107759 A107760
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 11 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
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