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Search: id:A080578
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| A080578 |
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a(1)=1; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+3 otherwise. |
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+0
13
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| 1, 4, 7, 8, 11, 14, 15, 16, 19, 22, 23, 26, 29, 30, 31, 32, 35, 38, 39, 42, 45, 46, 47, 50, 53, 54, 57, 60, 61, 62, 63, 64, 67, 70, 71, 74, 77, 78, 79, 82, 85, 86, 89, 92, 93, 94, 95, 98, 101, 102, 105, 108, 109, 110, 113, 116, 117, 120, 123, 124, 125, 126
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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More generally for fixed r, there is a nice connection between the sequence a(1)=1, a(n)=a(n-1)+1 if n is in the sequence, a(n)=a(n-1)+r+1 otherwise and the so-called metafibonacci sequences. Indeed, (a(n)-n)/r is a generalized metafibonacci sequence of order r as defined in Ruskey's recent paper (reference given at A046699). - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 04 2007
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LINKS
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B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
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FORMULA
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a(n) = 2n + O(1); a(2^n)=2^(n+1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 12 2003
a(1)=1 then for n>=2 a(n)=a(n+1-2^floor(log(n)/log(2)))+2*2^floor(log(n)/log(2))-1 ; (a(n)-n)/2=A046699(n) for n>=2. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 04 2007
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PROGRAM
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(PARI) a(n)=if(n<2, 1, a(n+1-2^floor(log(n)/log(2)))+2*2^floor(log(n)/log(2))-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 04 2007
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CROSSREFS
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Cf. A080455-A080458, A080036, A080037, A080468.
Sequence in context: A001494 A092214 A128373 this_sequence A047347 A137362 A024621
Adjacent sequences: A080575 A080576 A080577 this_sequence A080579 A080580 A080581
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KEYWORD
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nonn
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AUTHOR
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njas and Benoit Cloitre, Mar 23 2003
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