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 A001196 Double-bitters: only even length runs in binary expansion. 25
 0, 3, 12, 15, 48, 51, 60, 63, 192, 195, 204, 207, 240, 243, 252, 255, 768, 771, 780, 783, 816, 819, 828, 831, 960, 963, 972, 975, 1008, 1011, 1020, 1023, 3072, 3075, 3084, 3087, 3120, 3123, 3132, 3135, 3264, 3267, 3276, 3279, 3312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numbers whose set of base 4 digits is {0,3}. - Ray Chandler, Aug 03 2004 n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a power of 4 for every i. - Ray Chandler, Aug 03 2004 The first 2^n terms of the sequence could be obtained using the Cantor-like process for the segment [0,4^n-1]. E.g., for n=1 we have [0,{1,2},3] such that numbers outside of braces are the first 2 terms of the sequence; for n=2 we have [0,{1,2},3,{4,5,6,7,8,9,10,11},12,{13,14},15] such that the numbers outside of braces are the first 4 terms of the sequence, etc. - Vladimir Shevelev, Dec 17 2012 From Emeric Deutsch, Jan 26 2018: (Start) Also, the indices of the compositions having only even parts. For the definition of the index of a composition see A298644. For example, 195 is in the sequence since its binary form is 11000011 and the composition [2,4,2] has only even parts. 132 is not in the sequence since its binary form is 10000100 and the composition [1,4,1,2] has also odd parts. The command c(n) from the Maple program yields the composition having index n. (End) After the k-th step of generating the Koch snowflake curve, label the edges of the curve consecutively 0..3*4^k-1 starting from a vertex of the originating triangle. a(0), a(1), ... a(2^k-1) are the labels of the edges contained in one edge of the originating triangle. Add 4^k to each label to get the labels for the next edge of the triangle. Compare with A191108 in respect of the Sierpinski arrowhead curve. - Peter Munn, Aug 18 2019 LINKS Sean A. Irvine, Table of n, a(n) for n = 0..10000 R. Stephan, Some divide-and-conquer sequences ... R. Stephan, Table of generating functions Eric Weisstein's World of Mathematics, Koch Snowflake Wikipedia, Koch snowflake FORMULA a(2n) = 4*a(n), a(2n+1) = 4*a(n) + 3. a(n) = 3 * A000695(n). 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 3350 do if type(product(1+c(n)[j], j = 1 .. nops(c(n))), odd) = true 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 26 2018 MATHEMATICA fQ[n_] := Union@ Mod[Length@# & /@ Split@ IntegerDigits[n, 2], 2] == {0}; Select[ Range@ 10000, fQ] (* Or *) fQ[n_] := Union@ Join[IntegerDigits[n, 4], {0, 3}] == {0, 3}; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Dec 24 2012 *) PROG (Haskell) a001196 n = if n == 0 then 0 else 4 * a001196 n' + 3 * b             where (n', b) = divMod n 2 -- Reinhard Zumkeller, Feb 21 2014 (Python) def inA001196(n):     while n != 0:         if n%4 == 1 or n%4 == 2:             return 0         n = n//4     return 1 n, a = 0, 0 while n < 20:     if inA001196(a):         print(n, a)         n = n+1     a = a+1 # A.H.M. Smeets, Aug 19 2019 CROSSREFS 3 times the Moser-de Bruijn sequence A000695. Cf. A005823, A097252-A097262, A191108. Sequence in context: A022380 A290593 A005392 * A096854 A013191 A009783 Adjacent sequences:  A001193 A001194 A001195 * A001197 A001198 A001199 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane, based on an email from Bart la Bastide (bart(AT)xs4all.nl) STATUS approved

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)