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

1,1

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]

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.

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)

Example

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

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 *)

Crossrefs

Cf. A006852, A007063, A038807, A035486.

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

Sequence in context: A236213 A016694 A175038 * A244997 A274516 A202498

Adjacent sequences: A035502 A035503 A035504 * A035506 A035507 A035508

Keyword

nonn,tabf,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Dec 23 1999

Status

approved