Search: id:A006061
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%I A006061 M5385
%S A006061 1,121,11881,1164241,114083761,11179044361,1095432263641,
%T A006061 107341182792481,10518340481399521,1030690025994360601,
%U A006061 100997104206965939401,9896685522256667700721,969774184076946468731281
%N A006061 Star numbers (A003154) that are squares.
%D A006061 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 121, p. 42, Ellipses, 
               Paris 2008.
%D A006061 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, p. 22.
%D A006061 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006061 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A006061 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A006061 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StarNumber.html">Star Number</a>
%F A006061 A007667 = 3*square star numbers (A006061) + 2.
%F A006061 a(n) = denominator of kappa(sqrt(6)/A054320(n)) where kappa(x) is the 
               sum of successive remainders by computing the euclidean algorithm 
               for (1, x). - Thomas Baruchel (baruchel(AT)users.sourceforge.net), 
               Nov 29 2003
%F A006061 a(n) = 99(a(n-1) - a(n-2)) + a(n-3); a(n)=(5 - 2sqrt(6))/8*(sqrt(3) + 
               sqrt(2))^(4n) + (5 + 2sqrt(6))/8*(sqrt(3) - sqrt(2))^(4n) - 1/4. 
               - Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net) Feb 27 
               2000
%F A006061 a(n) = 98*a(n-1) - a(n-2) + 24. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 14 2008
%e A006061 a(2)=121 because this is the 2nd star number (A003154) that is a square.
%p A006061 Digits := 1000:q := seq(floor(evalf(( (5+2*sqrt(6))^n*(sqrt(6)-2)-(5-2*sqrt(6))^n*(sqrt(6)+2))^2/
               16)),n=1..100);
%p A006061 A006061:=-(1+22*z+z**2)/(z-1)/(z**2-98*z+1); [Conjectured (correctly) 
               by S. Plouffe in his 1992 dissertation.]
%Y A006061 A007667 is 3*a(n)+2, sqrt(a(n)) is A054320. Cf. A003154.
%Y A006061 Sequence in context: A006102 A036508 A054319 this_sequence A079215 A137466 
               A062689
%Y A006061 Adjacent sequences: A006058 A006059 A006060 this_sequence A006062 A006063 
               A006064
%K A006061 nonn,easy
%O A006061 1,2
%A A006061 N. J. A. Sloane (njas(AT)research.att.com).
%E A006061 More terms from Eric Weisstein (eric(AT)weisstein.com) and Sascha Kurz 
               (sascha.kurz(AT)uni-bayreuth.de), Mar 24 2002

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