id:A030302 - OEIS Search Results

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Write n in base 2 and juxtapose.

+0
8

1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1 (list; graph; listen)

	OFFSET	`1,1`
	FORMULA	`Let "index" i = ceiling( W(log(2)/2 (n - 1))/log(2) + 1 ) where W denotes the principal branch of the Lambert W function. Then a(n) = mod(floor(2^(mod(n + 2^i - 2, i) - i + 1) ceiling((n + 2^i - 1)/i - 1)), 2). See also Mathematica code. - David W. Cantrell (DWCantrell(AT)sigmaxi.net), Feb 19 2007`
	MATHEMATICA	`i[n_] := Ceiling[FullSimplify[ProductLog[Log[2]/2 (n - 1)]/Log[2] + 1]]; a[n_] := Mod[Floor[2^(Mod[n + 2^i[n] - 2, i[n]] - i[n] + 1) Ceiling[(n + 2^i[n] - 1)/i[n] - 1]], 2]; - David W. Cantrell (DWCantrell(AT)sigmaxi.net), Feb 19 2007`
	CROSSREFS	`Essentially same as A030190. Cf. A030303, ...` `Sequence in context: A014114 A014219 A065828 this_sequence A051023 A030657 A076213` `Adjacent sequences: A030299 A030300 A030301 this_sequence A030303 A030304 A030305`
	KEYWORD	`nonn,base`
	AUTHOR	`Clark Kimberling (ck6(AT)evansville.edu)`

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.

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