A194033 Inverse permutation of A194032; contains every positive integer exactly once.

1, 3, 6, 2, 5, 9, 10, 15, 4, 8, 13, 14, 20, 21, 28, 7, 12, 18, 19, 26, 27, 35, 36, 45, 11, 17, 24, 25, 33, 34, 43, 44, 54, 55, 66, 16, 23, 31, 32, 41, 42, 52, 53, 64, 65, 77, 78, 91, 22, 30, 39, 40, 50, 51, 62, 63, 75, 76, 89, 90, 104, 105, 120, 29

Offset: 1

Author

Clark Kimberling, Aug 12 2011

Keywords

• nonn

Links

• Zhuorui He, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A194032.

Programs

Mathematica

(See A194032.)

PARI

A194033(n)={my(x=sqrtint(n), y=n-x^2, z=min(y,floor(y/2+1))) ;binomial(x+z,2)+y+1} \\ Zhuorui He, Jul 19 2025

Formula

a(n) = binomial(x + z,2) + y + 1 where x = floor(sqrt(n)), y = n - x^2 and z = min(y,floor(y/2 + 1)). - Zhuorui He, Jul 19 2025

Extensions

a(63) corrected and a(64) added by Zhuorui He, Jul 07 2025