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A061579 Reverse one number (0), then two numbers (2,1), then three (5,4,3), then four (9,8,7,6), etc. 14
0, 2, 1, 5, 4, 3, 9, 8, 7, 6, 14, 13, 12, 11, 10, 20, 19, 18, 17, 16, 15, 27, 26, 25, 24, 23, 22, 21, 35, 34, 33, 32, 31, 30, 29, 28, 44, 43, 42, 41, 40, 39, 38, 37, 36, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 77, 76, 75, 74, 73, 72 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A self-inverse permutation of the nonnegative numbers.

a(n) is the smallest nonnegative integer not yet in the sequence such that n + a(n) is one less than a square. [Franklin T. Adams-Watters, Apr 06 2009]

From Michel Marcus, Mar 01 2021: (Start)

Array T(n,k) = (n+k)^2/2 + (n+3*k)/2 for n,k >=0 read by descending antidiagonals.

Array T(n,k) = (n+k)^2/2 + (3*n+k)/2 for n,k >=0 read by ascending antidiagonals. (End)

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

Madeline Brandt and Kåre Schou Gjaldbæk, Classification of Quadratic Packing Polynomials on Sectors of R^2, arXiv:2102.13578 [math.NT], 2021. See Figure 9 p. 17.

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = floor(sqrt(2n+1)-1/2)*floor(sqrt(2n+1)+3/2) - n = A005563(A003056(n)) - n.

MATHEMATICA

Module[{nn=20}, Reverse/@TakeList[Range[0, (nn(nn+1))/2], Range[nn]]]// Flatten (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jul 06 2018 *)

PROG

(PARI) default(realprecision, 100); for (n=0, 1000, f=floor(sqrt(2*n + 1) - 1/2); write("b061579.txt", n, " ", f*(f + 2) - n) ) \\ Harry J. Smith, Jul 25 2009

CROSSREFS

Fixed points are A046092.

Each reversal involves the numbers from A000217 through to A000096.

Cf. A038722. Transpose of A001477.

Sequence in context: A275131 A280513 A185023 * A094064 A159930 A058344

Adjacent sequences:  A061576 A061577 A061578 * A061580 A061581 A061582

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, May 21 2001

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)