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 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; text; 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. [Enrique Pérez Herrero, Apr 14 2010] REFERENCES R. K. Guy, Unsolved Problems Number Theory, Sect. E35. LINKS Enrique Pérez Herrero, Table of n, a(n) for n=1..10000 Clark Kimberling, Problem 1615, Crux Mathematicorum, Vol. 17 (2) 44 1991; Solution to Problem 1615, Crux Mathematicorum, Vol. 18, March 1992, p. 82-83. FORMULA From Enrique Pérez Herrero, 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 Enrique Pérez Herrero, 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. Cf. A175312, A074294, A000194, A006852, A007063. [Enrique Pérez Herrero, Apr 14 2010] Sequence in context: A236213 A016694 A175038 * A244997 A274516 A202498 Adjacent sequences:  A035502 A035503 A035504 * A035506 A035507 A035508 KEYWORD nonn,tabf,nice,easy,changed AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 23 1999 STATUS approved

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Last modified October 18 20:13 EDT 2019. Contains 328197 sequences. (Running on oeis4.)