A093573 Triangle read by rows: row n gives positions where n occurs in the Golay-Rudin-Shapiro related sequence A020986.
0, 1, 3, 2, 4, 6, 5, 7, 13, 15, 8, 12, 14, 16, 26, 9, 11, 17, 19, 25, 27, 10, 18, 20, 22, 24, 28, 30, 21, 23, 29, 31, 53, 55, 61, 63, 32, 50, 52, 54, 56, 60, 62, 64, 106, 33, 35, 49, 51, 57, 59, 65, 67, 105, 107, 34, 36, 38, 48, 58, 66, 68, 70, 104, 108, 110, 37, 39, 45, 47, 69, 71, 77, 79, 101, 103, 109, 111
Offset: 1
Examples
A020986(n) for n = 0, 1, ... is 1, 2, 3, 2, 3, 4, 3, 4, 5, 6, ..., so the positions of 1, 2, 3, 4, ... are 0; 1, 3; 2, 4, 6; 5, 7, 13, 15; ... From _Seiichi Manyama_, Apr 23 2017: (Start) Triangle begins: 0, 1, 3, 2, 4, 6, 5, 7, 13, 15, 8, 12, 14, 16, 26, 9, 11, 17, 19, 25, 27, 10, 18, 20, 22, 24, 28, 30, 21, 23, 29, 31, 53, 55, 61, 63, 32, 50, 52, 54, 56, 60, 62, 64, 106, 33, 35, 49, 51, 57, 59, 65, 67, 105, 107, 34, 36, 38, 48, 58, 66, 68, 70, 104, 108, 110, ... (End)
Links
- Reinhard Zumkeller, Rows n = 1..150 of triangle, flattened
- John Brillhart, Patrick Morton, Über Summen von Rudin-Shapiroschen Koeffizienten, (German) Illinois J. Math. 22 (1978), no. 1, 126--148. MR0476686 (57 #16245). - _N. J. A. Sloane_, Jun 06 2012
- Eric Weisstein's World of Mathematics, Rudin-Shapiro Sequence
Programs
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Haskell
a093573 n k = a093573_row n !! (k-1) a093573_row n = take n $ elemIndices n a020986_list a093573_tabl = map a093573_row [1..] -- Reinhard Zumkeller, Jun 06 2012
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Mathematica
With[{n = 16}, TakeWhile[#, Length@ #2 == #1 & @@ # &][[All, -1]] &@ Transpose@ {Keys@ #, Lookup[#, Keys@ #]} &[PositionIndex@ Accumulate@ Array[1 - 2 Mod[Length[FixedPointList[BitAnd[#, # - 1] &, BitAnd[#, Quotient[#, 2]]]], 2] &, n^2, 0] - 1]] // Flatten (* Michael De Vlieger, Jan 25 2020 *)
Extensions
Offset corrected by Reinhard Zumkeller, Jun 06 2012
Comments