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

1,3

Comments

Each positive integer n occurs n times, so the n-th row has length n.

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

Example

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)

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 *)

Prog

(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

Crossrefs

Column k=1 gives A212591. Diagonal k=n gives A020991.

Cf. A020985, A020986.

Sequence in context: A254107 A116942 A254108 * A126290 A277377 A227741

Adjacent sequences: A093570 A093571 A093572 * A093574 A093575 A093576

Keyword

nonn,tabl

Author

Eric W. Weisstein, Apr 01 2004

Extensions

Offset corrected by Reinhard Zumkeller, Jun 06 2012

Status

approved