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%I #47 Dec 31 2023 10:16:58
%S 0,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,
%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
%N a(0)=0, a(1)=1, a(n)=2 for n >= 2.
%C a(n) is also total number of positive integers below 10^(n+1) requiring 9 positive cubes in their representation as sum of cubes (cf. Dickson, 1939).
%C A061439(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + A181402(n) + A181404(n) + a(n) = A002283(n).
%C a(n) = number of obvious divisors of n. The obvious divisors of n are the numbers 1 and n. - _Jaroslav Krizek_, Mar 02 2009
%C Number of colors needed to paint n adjacent segments on a line. - _Jaume Oliver Lafont_, Mar 20 2009
%C a(n) = ceiling(n-th nonprimes/n) = ceiling(A018252(n)/A000027(n)) for n >= 1. Numerators of (A018252(n)/A000027(n)) in A171529(n), denominators of (A018252(n)/A000027(n)) in A171530(n). a(n) = A171624(n) + 1 for n >= 5. - _Jaroslav Krizek_, Dec 13 2009
%C a(n) is also the continued fraction for sqrt(1/2). - _Enrique Pérez Herrero_, Jul 12 2010
%C For n >= 1, a(n) = minimal number of divisors of any n-digit number. See A066150 for maximal number of divisors of any n-digit number. - _Jaroslav Krizek_, Jul 18 2010
%C Central terms in the triangle A051010. - _Reinhard Zumkeller_, Jun 27 2013
%H Leonard Eugene Dickson, <a href="http://projecteuclid.org/euclid.bams/1183502007">All integers except 23 and 239 are sums of eight cubes</a>, Bulletin of the American Mathematical Society 45 (1939), p. 588-591.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/WaringsProblem.html">MathWorld -- Waring's Problem.</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F G.f.: x*(1+x)/(1-x)=x*(1-x^2)/(1-x)^2. - _Jaume Oliver Lafont_, Mar 20 2009
%F a(n) = A000005(n) - A070824(n) for n >= 1.
%t A130130[0]:=0; A130130[1]:=1; A130130[n_]:=2; (* _Enrique Pérez Herrero_, Jul 12 2010 *)
%t A130130[n_]:=ContinuedFraction[Sqrt[1/2],n+1][[n+1]] (* _Enrique Pérez Herrero_, Jul 12 2010 *)
%t Join[{0, 1},LinearRecurrence[{1},{2},96]] (* _Ray Chandler_, Sep 23 2015 *)
%t PadRight[{0,1},120,{2}] (* _Harvey P. Dale_, Sep 15 2022 *)
%o (PARI) a(n)=min(n,2) \\ _Charles R Greathouse IV_, Jun 01 2011
%o (Haskell)
%o a130130 = min 2
%o a130130_list = 0 : 1 : repeat 2 -- _Reinhard Zumkeller_, Jun 27 2013
%Y Cf. A158411. - _Jaume Oliver Lafont_, Mar 20 2009
%K nonn,easy
%O 0,3
%A _Paul Curtz_, Aug 01 2007
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