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 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 (list; table; graph; refs; listen; history; text; internal format)
 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. 82-83. 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 EXTENSIONS More terms from James A. Sellers, Dec 23 1999 STATUS approved

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Last modified November 17 22:58 EST 2018. Contains 317279 sequences. (Running on oeis4.)