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 A087117 Number of zeros in the longest string of consecutive zeros in the binary representation of n. 14
 1, 0, 1, 0, 2, 1, 1, 0, 3, 2, 1, 1, 2, 1, 1, 0, 4, 3, 2, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 0, 5, 4, 3, 3, 2, 2, 2, 2, 3, 2, 1, 1, 2, 1, 1, 1, 4, 3, 2, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 0, 6, 5, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 4, 3, 2, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 5, 4, 3, 3, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The following four statements are equivalent: a(n) = 0; n = 2^k - 1 for some k > 0; A087116(n) = 0; A023416(n) = 0. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) = max(A007814(n), a(A025480(n-1))) for n >= 2. - Robert Israel, Feb 19 2017 a(2n+1) = a(n) (n>=1); indeed, the binary form of 2n+1 consists of the binary form of n with an additional 1 at the end - Emeric Deutsch, Aug 18 2017 MAPLE A087117 := proc(n)     local d, l, zlen ;     if n = 0 then         return 1 ;     end if;     d := convert(n, base, 2) ;     for l from nops(d)-1 to 0 by -1 do         zlen := [seq(0, i=1..l)] ;         if verify(zlen, d, 'sublist') then             return l ;         end if;     end do:     return 0 ; end proc; # R. J. Mathar, Nov 05 2012 MATHEMATICA nz[n_]:=Max[Length/@Select[Split[IntegerDigits[n, 2]], MemberQ[#, 0]&]]; Array[nz, 110, 0]/.-\[Infinity]->0 (* Harvey P. Dale, Sep 05 2017 *) PROG (Haskell) import Data.List (unfoldr, group) a087117 0       = 1 a087117 n   | null \$ zs n = 0   | otherwise   = maximum \$ map length \$ zs n where   zs = filter ((== 0) . head) . group .        unfoldr (\x -> if x == 0 then Nothing else Just \$ swap \$ divMod x 2) -- Reinhard Zumkeller, May 01 2012 CROSSREFS Cf. A023416, A007088, A007814. Cf. A025480, A038374, A090046, A090047, A090048, A090049, A090050. Sequence in context: A144789 A285097 A279209 * A029340 A288166 A126258 Adjacent sequences:  A087114 A087115 A087116 * A087118 A087119 A087120 KEYWORD nonn,base AUTHOR Reinhard Zumkeller, Aug 14 2003 STATUS approved

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Last modified March 26 20:42 EDT 2019. Contains 321534 sequences. (Running on oeis4.)