A064790 Inverse permutation to A060734.

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

Offset: 1

Author

N. J. A. Sloane, Oct 20 2001

Keywords

• nonn
• easy

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 ("ox-plowing") method - layer clockwise, layer counterclockwise and so. The same table A188568 read layer by layer clockwise is A194280. (End)

Examples

			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*r-1 numbers. (End)
		

Links

• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.
• Eric Weisstein's MathWorld, Pairing Function
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A060734, A064788, A188568, A194280.

Formula

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