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 A286574 Sum of the binary weights of the lengths of 1-runs in base-2 representation of n: a(n) = A000523(A286575(n)). 4
 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 3, 4, 2, 3, 3, 3, 3, 4, 2, 3, 1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 4, 3, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS a(0) = 0 (an empty sum). LINKS Antti Karttunen, Table of n, a(n) for n = 0..65536 FORMULA a(n) = A000523(A286575(n)). [Log_2 of run-length transform of A001316.] a(n) = A064547(A005940(1+n)). EXAMPLE For n = 27, "11011" in binary, there are two 1-runs, both of length 2, thus a(27) = A000120(2) + A000120(2) = 1 + 1 = 2. For n = 29, "11101" in binary, there are two 1-runs, of lengths 1 and 3, thus a(29) = A000120(1) + A000120(3) = 1 + 2 = 3. For n = 61, "111101" in binary, there are two 1-runs, of lengths 1 and 4, thus a(61) = A000120(1) + A000120(4) = 1 + 1 = 2. PROG (Scheme) (define (A286574 n) (A000523 (A286575 n))) (Python) from sympy import factorint, prime, log import math def wt(n): return bin(n).count("1") def a037445(n):     f=factorint(n)     return 2**sum([wt(f[i]) for i in f]) def A(n): return n - 2**int(math.floor(log(n, 2))) def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n)) def a286575(n): return a037445(b(n)) def a(n): return int(math.floor(log(a286575(n), 2))) # Indranil Ghosh, May 30 2017 CROSSREFS Cf. A000120, A000523, A001316, A005940, A064547, A286575. Sequence in context: A290085 A322867 A163109 * A316112 A317994 A128428 Adjacent sequences:  A286571 A286572 A286573 * A286575 A286576 A286577 KEYWORD nonn,base AUTHOR Antti Karttunen, May 28 2017 STATUS approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)