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 A035506 Stolarsky array read by antidiagonals. 52
 1, 2, 4, 3, 6, 7, 5, 10, 11, 9, 8, 16, 18, 15, 12, 13, 26, 29, 24, 19, 14, 21, 42, 47, 39, 31, 23, 17, 34, 68, 76, 63, 50, 37, 28, 20, 55, 110, 123, 102, 81, 60, 45, 32, 22, 89, 178, 199, 165, 131, 97, 73, 52, 36, 25, 144, 288, 322, 267, 212, 157, 118, 84, 58, 40, 27, 233, 466, 521, 432, 343, 254, 191, 136, 94, 65, 44, 30 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Inverse of sequence A064357 considered as a permutation of the positive integers. - Howard A. Landman, Sep 25 2001 PARI/GP script gives general solution for the Stolarsky array in square array form by row,column. Increase the default precision to compute large values in the array. - Randall L. Rathbun (randallr(AT)abac.com), Jan 25 2002 The Stolarsky array is the dispersion of the sequence s given by s(n)=(integer nearest n*x), where x=(golden ratio).  For a discussion of dispersions, see A191426. See A098861 for the row in which is a given number. - M. F. Hasler, Nov 05 2014 Named after the American mathematician Kenneth Barry Stolarsky. - Amiram Eldar, Jun 11 2021 REFERENCES C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138. LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened Clark Kimberling, Interspersions. Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, Vol. 117 (1993), pp. 313-321. David R. Morrison, A Stolarsky array of Wythoff pairs, A collection of manuscripts related to the Fibonacci sequence, Santa Clara, CA: Fibonacci Association, 1980, pp. 134-136. N. J. A. Sloane, Classic Sequences. Eric Weisstein's World of Mathematics, Stolarsky arrays. FORMULA T(1,k) = 2*T(0,k+1); T(3,k) = 3*T(0,k+2). - M. F. Hasler, Nov 05 2014 EXAMPLE Top left corner of the array is:    1    2    3    5    8   13   21   34   55    4    6   10   16   26   42   68  110  178    7   11   18   29   47   76  123  119  322    9   15   24   39   63  102  165  267  432   12   19   31   50   81  131  212  343  555   14   23   37   60   97  157  254  411  665 MAPLE A:= proc(n, k) local t, a, b; t:= (1+sqrt(5))/2; a:= floor(n*(t+1)+1 +t/2); b:= round(a*t); (Matrix([[b, a]]). Matrix([[1, 1], [1, 0]])^k) [1, 2] end: seq(seq(A (n, d-n), n=0..d), d=0..10); # Alois P. Heinz, Aug 17 2008 MATHEMATICA (* program generates the dispersion array T of the complement of increasing sequence f[n] *) r = 40; r1 = 12; (* r=# rows of T, r1=# rows to show *) c = 40; c1 = 12; (* c=# cols of T, c1=# cols to show *) x = GoldenRatio; f[n_] := Floor[n*x + 1/2] (* f(n) is complement of column 1 *) mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]] rows = {NestList[f, 1, c]}; Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}]; t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* t=Stolarsky array, A035506 *) Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* Stolarsky array as a sequence *) (* Program by Peter J. C. Moses, Jun 01 2011 *) PROG (PARI) {Stolarsky(r, c)= tau=(1+sqrt(5))/2; a=floor(r*(1+tau)-tau/2); b=round(a*tau); if(c==1, a, if(c==2, b, for(i=1, c-2, d=a+b; a=b; b=d; ); d))} CROSSREFS Cf. A035513 (Wythoff array), A035507 (inverse Stolarksy array), A191426. Sequence in context: A194030 A083044 A126714 * A246368 A316963 A320672 Adjacent sequences:  A035503 A035504 A035505 * A035507 A035508 A035509 KEYWORD nonn,tabl,easy,nice AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Sep 27 2000 Extended (terms, Mathematica, example) by Clark Kimberling, Jun 03 2011 Example corrected by M. F. Hasler, Nov 05 2014 STATUS approved

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Last modified May 17 23:07 EDT 2022. Contains 353779 sequences. (Running on oeis4.)