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 A044813 Positive integers having distinct base-2 run lengths. 10
 1, 3, 4, 6, 7, 8, 14, 15, 16, 24, 28, 30, 31, 32, 35, 39, 48, 49, 55, 57, 59, 60, 62, 63, 64, 67, 79, 96, 97, 111, 112, 120, 121, 123, 124, 126, 127, 128, 131, 135, 143, 159, 192, 193, 223, 224, 225, 239, 241, 247, 248, 249, 251, 252, 254, 255, 256, 259, 263 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A005811(a(n)) = A165413(a(n)). - Reinhard Zumkeller, Mar 02 2013 From Emeric Deutsch, Jan 25 2018: (Start) Also, the indices of the compositions that have distinct parts. For the definition of the index of a composition see A298644. For example, 223 is in the sequence since its binary form is 11011111 and the composition [2,1,5] has distinct parts. 100 is not in the sequence since its binary form is 1100100 and the parts of the composition [2,2,1,2] are not distinct. The command c(n) from the Maple program yields the composition having index n. (End) LINKS Reinhard Zumkeller and Gheorghe Coserea, Table of n, a(n) for n = 1..20000 (first 5000 terms from Reinhard Zumkeller) FORMULA a(Sum_{k=0..n} A032020(k)) = 2^n, for n>1. - Gheorghe Coserea, May 30 2017 MAPLE Runs := proc (L) local j, r, i, k: j := 1: r[j] := L: for i from 2 to nops(L) do if L[i] = L[i-1] then r[j] := r[j], L[i] else j := j+1: r[j] := L[i] end if end do: [seq([r[k]], k = 1 .. j)] end proc: RunLengths := proc (L) map(nops, Runs(L)) end proc: c := proc (n) ListTools:-Reverse(convert(n, base, 2)): RunLengths(%) end proc: A := {}: for n to 300 do if nops(convert(c(n), set)) = nops(c(n)) then A := `union`(A, {n}) else end if end do: A; # most of the Maple program is due to W. Edwin Clark. - Emeric Deutsch, Jan 25 2018 MATHEMATICA f[n_] := Unequal@@Length/@Split[IntegerDigits[n, 2]]; Select[Range, f] (* Ray Chandler, Oct 21 2011 *) PROG (Haskell) import Data.List (group, nub) a044813 n = a044813_list !! (n-1) a044813_list = filter p [1..] where    p x = nub xs == xs where          xs = map length \$ group \$ a030308_row x -- Reinhard Zumkeller, Mar 02 2013 (PARI) is(n) = {   my(v = 0, hist = vector(1 + logint(n+1, 2)));   while(n != 0,         v = valuation(n, 2); n >>= v; n++;         hist[v+1]++; if (hist[v+1] >= 2, return(0));         v = valuation(n, 2); n >>= v; n--;         hist[v+1]++; if (hist[v+1] >= 2, return(0)));   return(1); }; seq(n) = {   my(k = 1, top = 0, v = vector(n));   while(top < n, if (is(k), v[top++] = k); k++);   return(v); }; seq(59) \\ Gheorghe Coserea, Nov 02 2015 CROSSREFS Cf. A030308, A298644. Sequence in context: A239458 A007370 A322376 * A154661 A275672 A087753 Adjacent sequences:  A044810 A044811 A044812 * A044814 A044815 A044816 KEYWORD nonn,base AUTHOR EXTENSIONS Extended by Ray Chandler, Oct 21 2011 STATUS approved

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Last modified August 25 05:19 EDT 2019. Contains 326318 sequences. (Running on oeis4.)