A064788 Inverse permutation to A060736.

1, 2, 5, 3, 4, 8, 13, 9, 6, 7, 12, 18, 25, 19, 14, 10, 11, 17, 24, 32, 41, 33, 26, 20, 15, 16, 23, 31, 40, 50, 61, 51, 42, 34, 27, 21, 22, 30, 39, 49, 60, 72, 85, 73, 62, 52, 43, 35, 28, 29, 38, 48, 59, 71, 84, 98, 113, 99, 86, 74, 63, 53, 44, 36, 37, 47, 58, 70, 83, 97, 112

Offset: 1

Author

N. J. A. Sloane, Oct 20 2001

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A064790, A194280.

Programs

PARI

A064788(n)={my(t=sqrtint(n-1)+1); A000217(min(t,t^2-n+1)-2+n=min(t, n-(t-1)^2))+n} \\ recall: A000217(n)=(n+1)*n/2 \\ M. F. Hasler, Jan 13 2013

Formula

a(n) = (i+j-1)*(i+j-2)/2+j, 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

Extensions

More terms from David Wasserman, Jan 15 2002