

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
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OFFSET

0,2


COMMENTS

A selfinverse 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. AdamsWatters, 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



