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Search: id:A001614
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| A001614 |
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Connell sequence: 1 odd, 2 even, 3 odd, ...
(Formerly M0962 N0359)
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+0
26
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| 1, 2, 4, 5, 7, 9, 10, 12, 14, 16, 17, 19, 21, 23, 25, 26, 28, 30, 32, 34, 36, 37, 39, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 122
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Next (2n-1) odd numbers alternating with next 2n even numbers. Squares (A000290(n)) occur at the A000217(n)-th entry. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 06 2004. - Comment corrected by Daniel Forgues (squid(AT)zensearch.com), Jul 18 2009
a(t_n) = a(n(n+1)/2) = n^2 relates squares to triangular numbers. - Daniel Forgues
The natural numbers not included are A118011(n) = 4n - a(n) as n=1,2,3,... - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
As a triangle with row sums = A069778: (1, 6, 21, 52, 105,...):/Q 1;/Q 2, 4;/Q 5, 7, 9;/Q 10, 12, 14, 16;/Q ... [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
C. Pickover, Computers and the Imagination, St. Martin's Press, NY, 1991, p. 276.
Problem E1382, Amer. Math. Monthly, 67 (1960), 380.
C. A. Pickover, The Mathematics of Oz, Chapter 39, Camb. Univ. Press UK 2002.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Douglas E. Iannucci and Donna Mills-Taylor, On Generalizing the Connell Sequence, J. Integer Sequences, Vol. 2, 1999, #99.1.7.
Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, Vol. 1, 1998, #98.1.4.
Eric Weisstein's World of Mathematics, Connell Sequence
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FORMULA
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a(n) = 2n - [ (1+ sqrt (8n-7)) / 2 ].
a(n)=A005843(n) - A002024(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 06 2004
a(n) = A118012(A118011(n)). A117384( a(n) ) = n; A117384( 4n - a(n) ) = n. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
a(1)=1; then a(n)=a(n-1)+1 if a(n-1) is a square, a(n)=a(n-1)+2 otherwise. For example, a(21)=36 is a square therefore a(22)=36+1=37 which is not a square so a(23)=37+2=39 ... - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 07 2007
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MATHEMATICA
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lst={}; i=0; For[j=1, j<=4!, a=i+1; b=j; k=0; For[i=a, i<=9!, k++; AppendTo[lst, i]; If[k>=b, Break[]]; i=i+2]; j++ ]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 29 2008]
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CROSSREFS
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Cf. A117384, A118011 (complement), A118012.
A069778 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
Sequence in context: A121347 A106829 A083120 this_sequence A050731 A098794 A114055
Adjacent sequences: A001611 A001612 A001613 this_sequence A001615 A001616 A001617
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KEYWORD
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nonn,easy,nice,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 16 2001
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