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 A081601 Numbers n such that 3 does not divide Sum_{k=0..n} binomial(2k,k) = A006134(n). 5
 0, 3, 9, 12, 27, 30, 36, 39, 81, 84, 90, 93, 108, 111, 117, 120, 243, 246, 252, 255, 270, 273, 279, 282, 324, 327, 333, 336, 351, 354, 360, 363, 729, 732, 738, 741, 756, 759, 765, 768, 810, 813, 819, 822, 837, 840, 846, 849, 972, 975, 981, 984, 999, 1002, 1008, 1011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Apparently a(n)/3 mod 2 = A010060(n-1), the Thue-Morse sequence. a(n+1) is the smallest number with exactly n+1 partitions into distinct powers of 2 or of 3: A131996(a(n+1)) = n+1 and A131996(m) < n+1 for m < a(n+1). - Reinhard Zumkeller, Aug 06 2007 LINKS R. Stephan, Some divide-and-conquer sequences ... R. Stephan, Table of generating functions FORMULA Apparently a(n) = 3*A005836(n). G.f.: (x/(1 - x))*Sum_{k>=0} 3^(k+1)*x^(2^k)/(1 + x^(2^k)) (conjecture). - Ilya Gutkovskiy, Jul 23 2017 EXAMPLE For n=0, A006134(0) = 1, hence 0 is a term. MATHEMATICA Select[Range[0, 1020], Mod[Sum[Binomial[2 k, k], {k, 0, #}], 3] != 0 &] (* Michael De Vlieger, Nov 28 2015 *) PROG (PARI) for(n=0, 1e3, if(sum(k=0, n, binomial(2*k, k)) % 3 > 0, print1(n, ", "))) \\ Altug Alkan, Nov 26 2015 CROSSREFS Cf. A005836, A006134, A010060, A083096, A131996. Equals A089118(n-2) + 1, n > 1. Sequence in context: A303192 A261957 A261951 * A244018 A261950 A137344 Adjacent sequences:  A081598 A081599 A081600 * A081602 A081603 A081604 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Apr 22 2003 EXTENSIONS Zero prepended to the sequence and formulas modified accordingly by L. Edson Jeffery, Nov 25 2015 STATUS approved

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Last modified January 17 10:58 EST 2019. Contains 319218 sequences. (Running on oeis4.)