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Search: id:A064437
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| A064437 |
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a(1)=1, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise. |
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+0
13
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| 1, 3, 6, 8, 10, 13, 15, 18, 20, 23, 25, 27, 30, 32, 35, 37, 39, 42, 44, 47, 49, 51, 54, 56, 59, 61, 64, 66, 68, 71, 73, 76, 78, 80, 83, 85, 88, 90, 93, 95, 97, 100, 102, 105, 107, 109, 112, 114, 117, 119, 122, 124, 126, 129, 131, 134, 136, 138, 141, 143, 146, 148, 150
(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 let (x,y,z) be 3 positive integers and a(n) be the sequence a(1)=x, a(n)=a(n-1)+y if n is already in the sequence, a(n)=a(n-1)+z otherwise. Then it seems that a(n) is asymptotic to r*n where r is the largest positive root of q^2=z*q+z-y.
Example: (x,y,z) = (2, 1, 2) gives A004956(n), (x,y,z) = (1, 2, 3) gives A007066(n). The present sequence is the case (1, 3, 2).
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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) = ceiling((1+sqrt(2))*(n-1)+C) where C = 1/(2+sqrt(2)) = .292893218813...
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EXAMPLE
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a(6)=13 hence a(13)=a(12)+3=27+3=30
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PROGRAM
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(PARI) ?an=vector(100); an[1]=1; a(n)=if(n<0, 0, an[n]) ?x=1; y=3; z=2; an[1]=x; for(n=2, 100, an[n]=if(setsearch(Set(vector(n- 1, i, a(i))), n), a(n-1)+y, a(n-1)+z))
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CROSSREFS
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Cf. A004956, A007066, A026351, A079000. Apart from start, equals A080652 + 1.
Sequence in context: A128420 A099135 A047282 this_sequence A072149 A001066 A099518
Adjacent sequences: A064434 A064435 A064436 this_sequence A064438 A064439 A064440
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2003
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