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 A247282 Run Length Transform of A001317. 5
 1, 1, 1, 3, 1, 1, 3, 5, 1, 1, 1, 3, 3, 3, 5, 15, 1, 1, 1, 3, 1, 1, 3, 5, 3, 3, 3, 9, 5, 5, 15, 17, 1, 1, 1, 3, 1, 1, 3, 5, 1, 1, 1, 3, 3, 3, 5, 15, 3, 3, 3, 9, 3, 3, 9, 15, 5, 5, 5, 15, 15, 15, 17, 51, 1, 1, 1, 3, 1, 1, 3, 5, 1, 1, 1, 3, 3, 3, 5, 15, 1, 1, 1, 3, 1, 1, 3, 5, 3, 3, 3, 9, 5, 5, 15, 17, 3, 3, 3, 9, 3, 3, 9, 15, 3, 3, 3, 9, 9, 9, 15, 45 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Run Length Transform of a sequence {S(n), n>=0} is defined to be the sequence {T(n), n>=0} given by T(n) = Product_i S(i), where i runs through the lengths of runs of 1's in the binary expansion of n. E.g. 19 is 10011 in binary, which has two runs of 1's, of lengths 1 and 2. So T(19) = S(1)*S(2). T(0)=1 (the empty product). This sequence is obtained by applying Run Length Transform to the right-shifted version of the sequence A001317: 1, 3, 5, 15, 17, 51, 85, 255, 257, ... LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 FORMULA For all n >= 0, a(A051179(n)) = A246674(A051179(n)) = A051179(n). EXAMPLE 115 is '1110011' in binary. The run lengths of 1-runs are 2 and 3, thus a(115) = A001317(2-1) * A001317(3-1) = 3*5 = 15. From Omar E. Pol, Feb 15 2015: (Start) Written as an irregular triangle in which row lengths are the terms of A011782: 1; 1; 1,3; 1,1,3,5; 1,1,1,3,3,3,5,15; 1,1,1,3,1,1,3,5,3,3,3,9,5,5,15,17; 1,1,1,3,1,1,3,5,1,1,1,3,3,3,5,15,3,3,3,9,3,3,9,15,5,5,5,15,15,15,17,51; ... Right border gives 1 together with A001317. (End) MATHEMATICA a1317[n_] := FromDigits[ Table[ Mod[Binomial[n-1, k], 2], {k, 0, n-1}], 2]; Table[ Times @@ (a1317[Length[#]]&) /@ Select[Split[IntegerDigits[n, 2]], #[[1]] == 1&], {n, 0, 100}] (* Jean-François Alcover, Jul 11 2017 *) PROG (MIT/GNU Scheme) (define (A247282 n) (fold-left (lambda (a r) (* a (A001317 (- r 1)))) 1 (bisect (reverse (binexp->runcount1list n)) (- 1 (modulo n 2))))) ;; Other functions as in A227349. CROSSREFS Cf. A003714 (gives the positions of ones). Cf. A001317, A051179. A001316 is obtained when the same transformation is applied to A000079, the powers of two. Run Length Transforms of other sequences: A071053, A227349, A246588, A246595, A246596, A246660, A246661, A246674, A246685. Sequence in context: A218905 A027960 A319182 * A246685 A218618 A271451 Adjacent sequences:  A247279 A247280 A247281 * A247283 A247284 A247285 KEYWORD nonn AUTHOR Antti Karttunen, Sep 22 2014 STATUS approved

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Last modified June 2 14:21 EDT 2020. Contains 334787 sequences. (Running on oeis4.)