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2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Except for 1, n such that sum(k=1,n,(k mod 3)*C(n,k)) is a power of 2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 17 2002
The sequence 0,0,2,0,0,5,0,0,8,.. has a(n)=n(1+cos(2pi*n/3+pi/3)-sqrt(3)sin(2pi*n+pi/3))/3 and o.g.f. x^2(2+x^3)/(1-x^3)^2. - Paul Barry (pbarry(AT)wit.ie), Jan 28 2004. Artur Jasinski (grafix(AT)csl.pl), Dec 11 2007, remarks that this should read Table[(3n + 2)(1 + Cos[2Pi*(3n + 2)/3 + Pi/3] - Sqrt[3] Sin[2Pi*(3n + 2)/3 + Pi/3])/3, {n, 0,20}] .
Except for 2, exponents e such that x^e+x+1 is reducible.
a(n) = A125199(n+1,1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 24 2006
The trajectory of these numbers under iteration of sum of cubes of digits eventually turns out to be 371 or 407 (47 is the first of the second kind) [From Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 19 2009]
Union of A165334 and A165335. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 17 2009]
a(n) is the set of numbers congruent to{2,5,8} mod 9 [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 07 2010]
It appears that a(n)is the set of all values of y such that y^3 =kn+2 for integer k [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 08 2010]
Except for the first term, a(n) = ceil(A179896 / n) for n > 0 and remainder <> 0. [From Odimar Fabeny (aifab(AT)yahoo.com.br), Sep 08 2010]
These numbers do not occur in A000217 (triangular numbers). [Arkadiusz Wesolowski, Jan 08 2012]
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REFERENCES
| L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 16.
Konrad Knopp, Theory and Application of Infinite Series, Dover, p. 269
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LINKS
| L. Euler, Observatio de summis divisorum p. 9.
L. Euler, An observation on the sums of divisors p. 9.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 937
Tanya Khovanova, Recursive Sequences
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original German edition of "Theory and Application of Infinite Series")
Index entries for sequences related to linear recurrences with constant coefficients, signature (2,-1)
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FORMULA
| G.f.: (2+x)/(1-x)^2. a(n)=3+a(n-1).
sum(n=1, inf, (-1)^n/a(n))=1/3(Pi/sqrt(3)-ln(2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
1/2 - 1/5 + 1/8 - 1/11...= (1/3)*(Pi/sqrt(3) - ln 2). [Jolley] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 16 2006
sum_{n=0..infinity} 1/(a(2*n)*a(2*n+1)) = (Pi/sqrt(3)-log 2)/9 = 0.12451569... . [Jolley p. 48 eq (263)]
a(n)=2*a(n-1)-a(n-2); a(0)=2, a(1)=5. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=6*n-a(n-1)+1 with a(0)=2 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 25 2010]
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MATHEMATICA
| Range[2, 500, 3] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), May 26 2011 *)
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CROSSREFS
| A016789(n)=1+A016777(n).
First differences of A005449.
a(n)=A124388(n)/9.
Cf. A002939, A017041, A017485, A125202.
Cf. A017233.
Cf. A179896. [From Odimar Fabeny (aifab(AT)yahoo.com.br), Sep 08 2010]
Sequence in context: A078608 A189934 A189386 * A190082 A165334 A189512
Adjacent sequences: A016786 A016787 A016788 * A016790 A016791 A016792
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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