login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

REFERENCES

C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138.

LINKS

Alois P. Heinz, Antidiagonals n = 0..140, flattened

C. Kimberling, Interspersions

Clark Kimberling, Interspersions and dispersions, Proceedings of the American Mathematical Society, 117 (1993) 313-321.

N. J. A. Sloane, Classic Sequences

Eric Weisstein's World of Mathematics, Stolarsky arrays

Index entries for sequences that are permutations of the natural numbers

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 A006016 A227413

Adjacent sequences:  A035503 A035504 A035505 * A035507 A035508 A035509

KEYWORD

nonn,tabl,easy,nice

AUTHOR

N. J. A. Sloane

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 13 09:05 EST 2017. Contains 295957 sequences.