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 A051068 Partial sums of A014578. 4
 0, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 27, 28, 29, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 48, 49, 49 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Duplicate of A050294? [Joerg Arndt, Apr 27 2013] From Michel Dekking, Feb 10 2019: (Start) The answer to Joerg Arndt's question is: yes (modulo an offset). To see this, it suffices to prove that the two sequences of first differences Da and Db of a= A051068 and b:=A050294 are equal. Clearly the sequence Da of first differences of a is the sequence A014578. According to Philippe Deleham (2004), Da equals 0x = 0110110111110..., where x is the fixed point of the morphism 0->111, 1->110. From Vladimir Shevelev (2011) we know a formula for b=A050294: b(n) = n-b(floor(n/3)). This gives that the sequence of first differences Db:=(b(n+1)-b(n)) of b satisfies Db(3m+1) = Db(3m+2) = 1, and Db(3m+3) = 1 - Db(m). This implies that Db = x, the fixed point of 0->111, 1->110. (End) LINKS FORMULA a(3^n) = A015518(n+1) = -(-1)^n*A014983(n+1). - Philippe Deléham, Mar 31 2004 CROSSREFS Cf. A014578, A051069, A050294. Sequence in context: A127038 A175268 A241948 * A050294 A349775 A097950 Adjacent sequences: A051065 A051066 A051067 * A051069 A051070 A051071 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 3 00:23 EST 2022. Contains 358510 sequences. (Running on oeis4.)