|
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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 [From E. Perez Herrero (psychgeometry(AT)gmail.com), 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. 82-83.
|
|
|
LINKS
| E. Perez Herrero, Table of n, a(n) for n=1..10000
|
|
|
FORMULA
| Contribution from E. Perez Herrero (psychgeometry(AT)gmail.com), 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
| Contribution from E. Perez Herrero (psychgeometry(AT)gmail.com), 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 E. Perez Herrero (psychgeometry(AT)gmail.com), Apr 14 2010]
Sequence in context: A205111 A016694 A175038 * A202498 A143308 A163238
Adjacent sequences: A035502 A035503 A035504 * A035506 A035507 A035508
|
|
|
KEYWORD
| nonn,tabf,nice,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
|
| |
|
|
