

A035505


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


2



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
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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*i3 [From Enrique Pérez Herrero, Apr 14 2010]


REFERENCES

R. K. Guy, Unsolved Problems Number Theory, Sect. E35.
C. Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991 and Vol. 18, March 1992, p. 8283.


LINKS

E. Pérez Herrero, Table of n, a(n) for n=1..10000


FORMULA

From Enrique Pérez Herrero, Apr 14 2010: (Start)
a(n)=K(A000194(n)+2,A074294(n)), where:
K(i,j)=i+j1; (j>=2*i3)
K(i,j)=K(i1,i(j+2)/2); If j is Even and (j<2*i3)
K(i,j)=K(i1,i+(j1)/2); If j is Odd and (j<2*i3) (End)


EXAMPLE

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


MATHEMATICA

Contribution from Enrique Pérez Herrero, Apr 14 2010: (Start)
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]] (End)


CROSSREFS

Cf. A006852, A007063, A038807, A035486.
A175312,A074294,A000194,A006852,A007063 [From 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



