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A007063
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Main diagonal of Kimberling's expulsion array (A035486).
(Formerly M2387)
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7
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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; internal format)
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OFFSET
| 1,2
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REFERENCES
| R. K. Guy, Unsolved Problems Number Theory, Sect E35.
C. Kimberling, Problem 1615, Crux Mathematicorum (Ottawa), Vol. 17 (2) 44 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| E. Perez Herrero, Table of n, a(n) for n=1..100000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
| a(theta(k))=3*theta(k)-(k+1), where theta(k)=sum_{i=0}^{k-1}{2^floor(i/3)} [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Feb 23 2010]
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MATHEMATICA
| Contribution from Enrique Perez Herrero (psychgeometry(AT)gmail.com), Feb 09 2010: (Start)
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] (End)
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PROG
| Contribution from Enrique Perez Herrero (psychgeometry(AT)gmail.com), Feb 21 2010: (Start)
(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); (End)
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CROSSREFS
| Cf. A175312 [From Enrique Perez Herrero (psychgeometry(AT)gmail.com), Mar 30 2010]
Sequence in context: A075380 A177983 A078439 * A127397 A201271 A167808
Adjacent sequences: A007060 A007061 A007062 * A007064 A007065 A007066
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
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