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A090740
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Exponent of 2 in 3^n - 1.
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6
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1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 8, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 6, 1, 3, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 7, 1, 3, 1, 4, 1, 3, 1, 5, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The 2-adic order of Fibonacci(3n) [Lengyel]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]
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LINKS
| T. Lengyel, The order of the Fibonacci and Lucas numbers, Fib. Quart. 33 (1995), 234-239. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]
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FORMULA
| Multiplicative with a(p^e) = e+2 if p = 2; 1 if p > 2. G.f.: A(x) = 1/(1-x^2) + sum_{k=0..infinity} x^(2^k)/(1-x^(2^k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 19 2004
G.f.: sum_{k=0..inf} t(1+2t+t^2+t^3)/(1-t^4) with t=x^2^k. Recurrence: a(2n) = a(n) + 1 + [n odd], a(2n+1) = 1. (Ralf Stephan, Jan 23 2004)
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EXAMPLE
| n=2: -1+3^2=8.1 so a(2)=3;
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MATHEMATICA
| Table[Part[Flatten[FactorInteger[ -1+3^n]], 2], {n, 1, 70}]
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PROG
| a(n)=if(n<1, 0, if(n%2==0, a(n/2)+1+(n/2)%2, 1)) (Ralf Stephan, Jan 23 2004)
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CROSSREFS
| Cf. A069895, A091512, A088660, A090739.
Cf. A001511.
a(n) = A007814(n) + A059841(n) + 1.
Sequence in context: A030757 A004592 A116992 * A094603 A165595 A143825
Adjacent sequences: A090737 A090738 A090739 * A090741 A090742 A090743
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KEYWORD
| nonn,mult
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AUTHOR
| Labos E. and R. Stephan ((labos(AT)ana.sote.hu) and (ralf(AT)ark.in-berlin.de)), Jan 19 2004
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