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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 the next row, start with the first element to the right of the diagonal term, then take the first to the left of the diagonal, then the second to the right, then the second to the left, the third to the right, etc. It is conjectured since 1992 that the main diagonal elements (A007063) are a permutation of the positive integers. REFERENCES R. K. Guy, Unsolved Problems Number Theory, Sect E35. LINKS Enrique 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. Enrique Pérez Herrero, Formulas and programs for Kimberling's expulsion array Clark 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 The array starts (with elements of A007063 in brackets):   [1]  2   3   4   5   6   7   8   9  10  11. 12 ...    2  [3]  4   5   6   7   8   9  10  11  12  13 ...    4   2  [5]  6   7   8   9  10  11  12  13  14 ...    6   2   7  [4]  8   9  10  11  12  13  14  15 ...    8   7   9   2 [10]  6  11  12  13  14  15  16 ...    6   2  11   9  12  [7] 13   8  14  15  16  17 ...   13  12   8   9  14  11 [15]  2  16   6  17  18 ... 2 occurs as diagonal element in row 25, 27 in row 7598, and 19 in row 49595 (cf. A006852). 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 (positions), A007063 (main diagonal), A035505 (active part), A038807. Cf. A175312 (maximum value on lower shuffle part). 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 Edited by Georg Fischer, Jul 03 2020 STATUS approved

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Last modified August 9 20:24 EDT 2020. Contains 336326 sequences. (Running on oeis4.)