

A035486


Kimberling's expulsion array read by antidiagonals.


8



1, 2, 2, 3, 3, 4, 4, 4, 2, 6, 5, 5, 5, 2, 8, 6, 6, 6, 7, 7, 6, 7, 7, 7, 4, 9, 2, 13, 8, 8, 8, 8, 2, 11, 12, 2, 9, 9, 9, 9, 10, 9, 8, 11, 18, 10, 10, 10, 10, 6, 12, 9, 16, 17, 16, 11, 11, 11, 11, 11, 7, 14, 14, 12, 14, 23, 12, 12, 12, 12, 12, 13, 11, 6, 9, 21, 2, 13, 13, 13, 13, 13, 13, 8, 15
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OFFSET

1,2


COMMENTS

To get next row, start with element to right of diagonal term, then take number to left of diagonal, then back to 2nd number to right, etc.


REFERENCES

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


LINKS

E. Pérez Herrero, Table of n, a(n) for n = 1..10000
D. Gale, Tracking the Automatic Ant: And Other Mathematical Explorations, ch. 5, p. 27. Springer, 1998.
C. Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991 and Vol. 18, March 1992, p. 8283.
Eric Weisstein's World of Mathematics, Kimberling Sequence


EXAMPLE

1 2 3 4 5 6 7 8 9 10 ...
2 3 4 5 6 7 8 9 10 11 ...
4 2 5 6 7 8 9 10 11 12 ...
6 2 7 4 8 9 10 11 12 13 ...
8 7 9 2 10 6 11 12 13 14 ...


MATHEMATICA

From Enrique Pérez Herrero, Mar 30 2010: (Start)
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));
K[i_] := K[i] = K[i, i]; SetAttributes[K, Listable];
T[n_] := n*(n + 1)/2;
S[n_] := Floor[1/2 (1 + Sqrt[1 + 8 (n  1)])];
AJ[n_] := 1 + T[S[n]]  n;
AI[n_] := 1 + S[n]  AJ[n];
A035486[n_] := K[AI[n], AJ[n]]; (End)


CROSSREFS

Cf. A006852, A007063, A038807.
Cf. A175312.
Sequence in context: A085654 A074719 A079730 * A282347 A172397 A237815
Adjacent sequences: A035483 A035484 A035485 * A035487 A035488 A035489


KEYWORD

nonn,tabl,nice,look,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from James A. Sellers, Dec 23 1999


STATUS

approved



