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Search: id:A001651
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| A001651 |
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Not divisible by 3.
(Formerly M0957 N0357)
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+0
40
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| 1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98, 100, 101, 103, 104
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Inverse binomial transform of A084858. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2003
Earliest monotonic sequence starting with (1,2) and satisfying the condition : "a(n)+a(n-1) is not in the sequence" - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 25 2004
a(0) = 1; a(n) is least number which is relatively prime to the sum of all the previous terms. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 18 2001
For n>2, numbers having 3 as an anti-divisor. - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Oct 02 2005
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REFERENCES
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L. Carlitz, R. Scoville and T. Vaughan, Some arithmetic functions related to Fibonacci numbers, Fib. Quart., 11 (1973), 337-386.
G. Ledin, Jr., Is Eratosthenes out?, Fib. Quart., 6 (No. 4, 1968), 261-265.
M. A. Nyblom, Some curious sequences ..., Am. Math. Monthly 109 (#6, 200), 559-564, Ex. 2.2.
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LINKS
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A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004. (See Table 5.)
G. P. Michon, Counting Polyhedra
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, RATS Sequence
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FORMULA
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a(n) = 3+a(n-2). a(n) = a(n-1)+a(n-2)-a(n-3). a(2n) = 3n+1, a(2n-1) = 3n-1.
G.f.: (1+x+x^2)/((1-x)*(1-x^2)) - Michael Somos, Jun 08, 2000
a(n) = (4-n)*a(n-1)+2*a(n-2)+(n-3)*a(n-3) (from the Carlitz et al. article).
a(n)=Floor[(3n+2)/2]
a(1)=1, a(n) = 2*a(n-1)- 3*floor(a(n-1)/3). - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 17 2002
a(n) = 1 + n - n mod 2 + (n + n mod 2)/2. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Dec 17 2002
a(0) = 1, a(n+1) = a(n) + a(n) mod 3. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Mar 23 2003
a(0)=1, a(n)=3n-a(n-1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 12 2003
a(n)=3(2n+1)/4+(-1)^n/4 - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2003
Nearest integer to sum(k>n, 1/k^3)/sum(k>n, 1/k^4) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2003
Partial sums of A040001. a(n)=A032766(n)-1. - Paul Barry (pbarry(AT)wit.ie), Sep 02 2003
a(n)=T(n+1, 1)=T(n+1, n), where T is the array in A026386. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 18 2004
a(n)=sqrt(3 A001082(n)+1 ) - Zak Seidov (zakseidov(AT)yahoo.com), Dec 12 2007
a(n) = A077043(n+1) - A077043(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 28 2007
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MAPLE
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A001651 := n -> 3*floor((n+1)/2) + (-1)^n;
A001651:=(1+z+z**2)/(z+1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
a[0]:=1:a[1]:=2:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..69); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
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PROGRAM
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(PARI) a(n)= 1+n+n\2
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CROSSREFS
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Differs from A059564 after 35= a(23)= A059564(24).
Cf. A026386, A001082.
Cf. A007494, A032766, A000726, A003105.
Adjacent sequences: A001648 A001649 A001650 this_sequence A001652 A001653 A001654
Sequence in context: A054386 A127450 A059564 this_sequence A003253 A119905 A067940
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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