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 A087116 Number of maximal groups of consecutive zeros in binary representation of n. 15
 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS The following four statements are equivalent: a(n) = 0; n = 2^k - 1 for some k; A087117(n) = 0; A023416(n) = 0. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A033264(n) for n > 0 since strings of 0's alternate with strings of 1's. - Jonathan Sondow, Jan 17 2016 a(n) = a(2*n + 1) = a(4*n + 2) - 1, if n > 0. - Michael Somos, Nov 04 2016 a(n) = A069010(A003817(n)-n) for n > 0. - Chai Wah Wu, Nov 04 2016 EXAMPLE G.f. = 1 + x^2 + x^4 + x^5 + x^6 + x^8 + x^9 + 2*x^10 + x^11 + x^12 + x^13 + x^14 + ... PROG (Haskell) a087116 0 = 1 a087116 n = f 0 n where    f y 0 = y    f y x = if r == 0 then g x' else f y x'            where (x', r) = divMod x 2                  g z = if r == 0 then g z' else f (y + 1) z'                        where (z', r) = divMod z 2 -- Reinhard Zumkeller, Mar 31 2015 (PARI) a(n) = if (n == 0, 1, hammingweight(bitxor(n, n>>1)) >> 1); vector(102, i, a(i-1))  \\ Gheorghe Coserea, Sep 17 2015 (Python) def A087116(n):     return sum(1 for d in bin(n)[2:].split('1') if len(d)) # Chai Wah Wu, Nov 04 2016 CROSSREFS Cf. A087118, A087119, A087120, A023416, A007088. Essentially the same as A033264. Sequence in context: A025449 A047988 A037818 * A033264 A258045 A239302 Adjacent sequences:  A087113 A087114 A087115 * A087117 A087118 A087119 KEYWORD nonn AUTHOR Reinhard Zumkeller, Aug 14 2003 STATUS approved

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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)