

A064790


Inverse permutation to A060734.


4



1, 3, 5, 2, 6, 9, 13, 8, 4, 10, 14, 19, 25, 18, 12, 7, 15, 20, 26, 33, 41, 32, 24, 17, 11, 21, 27, 34, 42, 51, 61, 50, 40, 31, 23, 16, 28, 35, 43, 52, 62, 73, 85, 72, 60, 49, 39, 30, 22, 36, 44, 53, 63, 74, 86, 99, 113, 98, 84, 71, 59, 48, 38, 29, 45, 54, 64, 75, 87, 100, 114
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OFFSET

1,2


COMMENTS

From Boris Putievskiy, Mar 14 2013: (Start)
a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers.
Layer is pair of sides of square from T(1,n) to T(n,n) and from T(n,n) to T(n,1). This sequence is A188568 as table read by boustrophedonic ("oxplowing") method  layer clockwise, layer counterclockwise and so. The same table A188568 read layer by layer clockwise is A194280. (End)


LINKS

Table of n, a(n) for n=1..71.
Index entries for sequences that are permutations of the natural numbers
Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO]
Eric Weisstein's MathWorld, Pairing Function


FORMULA

a(n) = (i+j1)*(i+j2)/2+i, where i=min(t; t^2n+1), j=min(t; n(t1)^2), t=floor(sqrt(n1))+1.  Boris Putievskiy, Dec 24 2012


EXAMPLE

From Boris Putievskiy, Mar 14 2013: (Start)
The start of the sequence as table:
1....2...6...7..15..16..28...
3....5...9..12..20..23..35...
4....8..13..18..26..31..43...
10..14..19..25..33..40..52...
11..17..24..32..41..50..62...
21..27..34..42..51..61..73...
22..30..39..49..60..72..85...
. . .
The start of the sequence as triangular array read by rows:
1;
3,5,2;
6,9,13,8,4;
10,14,19,25,18,12,7;
15,20,26,33,41,32,24,17,11;
21,27,34,42,51,61,50,40,31,23,16;
28,35,43,52,62,73,85,72,60,49,39,30,22;
. . .
Row number r contains 2*r1 numbers. (End)


CROSSREFS

Cf. A060734, A064788, A188568, A194280.
Sequence in context: A010782 A333111 A139584 * A113966 A164611 A316086
Adjacent sequences: A064787 A064788 A064789 * A064791 A064792 A064793


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 20 2001


STATUS

approved



