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Search: id:A105183
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| A105183 |
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a(n) = 1 + a(n-1)*{a(n-1) + 1}, with a(0)=2. |
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1
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| 2, 7, 57, 3307, 10939557, 119673918295807, 14321846720271609085072077057, 205115293478954645768397227034180943592279329877217858307, 42072283618957694230389567430137958296609066493047345973782287300661413651741392\ 431587718724877522268597146764557
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For n>1, a(n) has digital root 3 or 4 depending on whether n is odd or even.
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REFERENCES
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T. Koshy, "Intriguing Properties Of Three Related Number Sequences",in Journal of Recreational Mathematics, vol. 32(3) 210-3 2003-4 Baywood NY.
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FORMULA
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For n>0, a(n) = Sum(k=0,n-1,a(k)^2) + n + 2. Conjecture: a(n) is asymptotic to d - 1/2 -(5/2^3)/d -(65/2^7)/d^3 -(650/2^11)/d^5 -(19045/2^15)/d^7 -(274950/2^19)/d^9 -(6979050/2^23)/d^11 -(130292500/2^27)/d^13 ... where d = c^(2^n) and c is a constant = 1.288203192684485177845610784851700404829443712770079185959554466777577486352420255603915828361833141546.... - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Dec 12 2007
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MAPLE
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a[0]:=2: for n from 1 to 8 do a[n]:=1+a[n-1]*(a[n-1]+1) od: seq(a[n], n=0..8); (Deutsch)
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CROSSREFS
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Cf. A005267.
Sequence in context: A048898 A034935 A121079 this_sequence A023364 A120952 A083810
Adjacent sequences: A105180 A105181 A105182 this_sequence A105184 A105185 A105186
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 11 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 13 2005
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