A066181 Permutation of the integers with cycle form {1}, {2, 3}, {4, 5, 6}, {7, 8, 9, 10}, ...

1, 3, 2, 5, 6, 4, 8, 9, 10, 7, 12, 13, 14, 15, 11, 17, 18, 19, 20, 21, 16, 23, 24, 25, 26, 27, 28, 22, 30, 31, 32, 33, 34, 35, 36, 29, 38, 39, 40, 41, 42, 43, 44, 45, 37, 47, 48, 49, 50, 51, 52, 53, 54, 55, 46, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 56, 68, 69, 70, 71, 72, 73

Offset: 1

Author

Wouter Meeussen, Dec 15 2001

Keywords

• easy
• nonn
• tabl

Comments

Arrange natural numbers 1,2,3,4,5,... as a triangle like A000027, then rotate each row of triangle one left. - Antti Karttunen, May 07 2002

For a group of n terms a^(n)(k)= k where n(n-1)/2 < k <= n(n+1)/2. E.g. for the three terms 5, 6 and 4, a(5)= 6, a(6) = 4, a(4) = 5; a(a(a(5))) = 5 = a^(3)(5). - Amarnath Murthy, May 31 2003

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse permutation: A066182.

Programs

Maple

a := proc(n) floor(sqrt(2*n));n+1;`if`(2*n=%%*(%%+1),%-%%,%) end: # Peter Luschny, Jan 25 2017

Mathematica

FromCycles[Table[n(n-1)/2+Range[n], {n, 13}]]

Formula

a(n) = 1 + n + binomial(round(sqrt(2*n)),2) - binomial(round(sqrt(2*n+2)),2). - Brian Tenneson, Jan 23 2017