A035505 Active part of Kimberling's expulsion array as a triangular array.

4, 2, 6, 2, 7, 4, 8, 7, 9, 2, 10, 6, 6, 2, 11, 9, 12, 7, 13, 8, 13, 12, 8, 9, 14, 11, 15, 2, 16, 6, 2, 11, 16, 14, 6, 9, 17, 8, 18, 12, 19, 13, 18, 17, 12, 9, 19, 6, 13, 14, 20, 16, 21, 11, 22, 2, 16, 14, 21, 13, 11, 6, 22, 19, 2, 9, 23, 12, 24, 17, 25, 18, 23, 2, 12, 19, 24, 22, 17, 6

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• tabf
• nice
• easy

Comments

Active or shuffle part of Kimberling's expulsion array (A035486) is given by the elements K(i,j), where j < 2*i-3. [Enrique Pérez Herrero, Apr 14 2010]

Examples

			4 2; 6 2 7 4; 8 7 9 2 10 6; ...
		

References

• R. K. Guy, Unsolved Problems Number Theory, Sect. E35.

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..10000
• Clark Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991; Solution to Problem 1615, Crux Mathematicorum, Vol. 18, March 1992, p. 82-83.

Crossrefs

Cf. A006852, A007063, A038807, A035486.

Cf. A175312, A074294, A000194, A006852, A007063. [Enrique Pérez Herrero, Apr 14 2010]

Programs

Mathematica

A000194[n_] := Floor[(1 + Sqrt[4 n - 3])/2];
A074294[n_] := n - 2*Binomial[Floor[1/2 + Sqrt[n]], 2];
K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);
K[i_, j_] := K[i - 1, i - (j + 2)/2] /; (EvenQ[j] && (j < 2 i - 3));
K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));
A035505[n_] := K[A000194[n] + 2, A074294[n]]
(* Enrique Pérez Herrero, Apr 14 2010 *)

Formula

From Enrique Pérez Herrero, Apr 14 2010: (Start)

a(n) = K(A000194(n)+2, A074294(n)), where

K(i,j) = i + j - 1; (j >= 2*i - 3)

K(i,j) = K(i-1, i-(j+2)/2) if j is even and j < 2*i - 3

K(i,j) = K(i-1, i+(j-1)/2); if j is odd and j < 2*i - 3.

(End)

Extensions

More terms from James Sellers, Dec 23 1999