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2, 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Let s(n)=sum(k>=1,1/n^(2^k)). Then I conjecture that the maximum element in the continued fraction for s(n) is n^2+2. - Benoit Cloitre, Aug 15, 2002.
Binomial transformation yields A081908, with A081908(0)=1 dropped. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 05 2008]
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 0..1000
Hesam Dashti, A New Upper Bound on the Length of Shortest Permutation Strings; An Algorithm for Generating Permutation Strings, Sep 26, 2010. - Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 28 2010
Guo-Niu Han, Enumeration of Standard Puzzles
Eric Weisstein's World of Mathematics, Near-Square Prime
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| G.f.: (2-3x+3x^2)/(1-x)^3. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 05 2008]
a(n) = ((n-2)^2 + 2*(n+1)^2)/3. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 13 2009]
a(n) = A000196(A156798(n) - A000290(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 16 2009]
a(n) = 2*n+a(n-1)-1 with a(0)=2. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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MAPLE
| with(combinat, fibonacci):seq(fibonacci(3, i)+1, i=0..49); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
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MATHEMATICA
| a[n_]:=n^2+2; [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 15 2008]
LinearRecurrence[{3, -3, 1}, {2, 3, 6}, 50] (* Vincenzo Librandi, Feb 15 2012 *)
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PROG
| (Other) sage: [lucas_number1(3, n, -2) for n in xrange(0, 50)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
(PARI) { for (n = 0, 1000, write("b059100.txt", n, " ", n^2+2); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 24 2009]
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CROSSREFS
| Cf. A000290, A002522, A056899. Apart from initial terms, same as A010000.
Cf. A069987 [From Vincenzo Librandi, Feb 11 2009]
Sequence in context: A049794 A121617 A157656 * A131512 A147388 A180712
Adjacent sequences: A059097 A059098 A059099 * A059101 A059102 A059103
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Feb 13 2001
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