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A007063 Main diagonal of Kimberling's expulsion array (A035486).
(Formerly M2387)
9
1, 3, 5, 4, 10, 7, 15, 8, 20, 9, 18, 24, 31, 14, 28, 22, 42, 35, 33, 46, 53, 6, 36, 23, 2, 55, 62, 59, 76, 65, 54, 11, 34, 48, 70, 79, 99, 95, 44, 97, 58, 84, 25, 13, 122, 83, 26, 115, 82, 91, 52, 138, 67, 90, 71, 119, 64, 37, 81, 39, 169, 88, 108, 141, 38, 16, 146, 41, 21 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

D. Gale, Tracking the Automatic Ant: And Other Mathematical Explorations, ch. 5, p. 27. Springer, 1998.

R. K. Guy, Unsolved Problems Number Theory, Sect E35. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..100000

Clark Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991; Solution to Problem 1615, Crux Mathematicorum, Vol. 18, March 1992, pp. 82-83.

Eric Weisstein's World of Mathematics, Kimberling Sequence

FORMULA

a(theta(k)) = 3*theta(k)-(k+1), where theta(k) = Sum_{i=0..k-1} 2^floor(i/3). - Enrique Pérez Herrero, Feb 23 2010

MATHEMATICA

K[i_, j_] := i + j - 1 /; (j >= 2 i - 3);

K[i_, j_] := K[i - 1, i - j/2 - 1] /; (EvenQ[j] && (j < 2 i - 3));

K[i_, j_] := K[i - 1, i + (j - 1)/2] /; (OddQ[j] && (j < 2 i - 3));

A007063[i_] := A007063[i] = K[i, i]; SetAttributes[A007063, Listable] (* Enrique Pérez Herrero, Feb 09 2010 *)

PROG

(PARI) K(i, j) = { my(i1, j1); i1=i; j1=j;

while(j1<(2*i1-3), if(j1%2, j1=i1+((j1-1)/2), j1=i1-((j1+2)/2)); i1--; );

return(i1+j1-1); }

A007063(i)=K(i, i); \\ Enrique Pérez Herrero, Feb 21 2010

CROSSREFS

Cf. A175312, A006852, A035486, A038807.

Sequence in context: A177983 A294673 A078439 * A335500 A127397 A284048

Adjacent sequences:  A007060 A007061 A007062 * A007064 A007065 A007066

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from James A. Sellers, Dec 23 1999

STATUS

approved

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Last modified August 13 22:34 EDT 2020. Contains 336465 sequences. (Running on oeis4.)