A130130 a(0)=0, a(1)=1, a(n)=2 for n >= 2.

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, 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, 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

Offset: 0

Author

Paul Curtz, Aug 01 2007

Keywords

• nonn
• easy

Comments

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).

A061439(n) + A181375(n) + A181377(n) + A181379(n) + A181381(n) + A181400(n) + A181402(n) + A181404(n) + a(n) = A002283(n).

a(n) = number of obvious divisors of n. The obvious divisors of n are the numbers 1 and n. - Jaroslav Krizek, Mar 02 2009

Number of colors needed to paint n adjacent segments on a line. - Jaume Oliver Lafont, Mar 20 2009

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

a(n) is also the continued fraction for sqrt(1/2). - Enrique Pérez Herrero, Jul 12 2010

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

Central terms in the triangle A051010. - Reinhard Zumkeller, Jun 27 2013

Decimal expansion of 11/900. - Elmo R. Oliveira, May 05 2024

Links

• Leonard Eugene Dickson, All integers except 23 and 239 are sums of eight cubes, Bulletin of the American Mathematical Society 45 (1939), p. 588-591.
• Eric Weisstein's World of Mathematics, Waring's Problem.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A000005, A000027, A002283, A018252, A051010, A061439, A066150, A070824, A158411, A171529, A171530, A171624, A181375, A181377, A181379, A181381, A181400, A181402, A181404.

Programs

Haskell

a130130 = min 2
a130130_list = 0 : 1 : repeat 2  -- Reinhard Zumkeller, Jun 27 2013

Mathematica

A130130[0]:=0; A130130[1]:=1; A130130[n_]:=2; (* Enrique Pérez Herrero, Jul 12 2010 *)
A130130[n_]:=ContinuedFraction[Sqrt[1/2],n+1][[n+1]] (* Enrique Pérez Herrero, Jul 12 2010 *)
Join[{0, 1},LinearRecurrence[{1},{2},96]] (* Ray Chandler, Sep 23 2015 *)
PadRight[{0,1},120,{2}] (* Harvey P. Dale, Sep 15 2022 *)

PARI

a(n)=min(n,2) \\ Charles R Greathouse IV, Jun 01 2011

Formula

G.f.: x*(1+x)/(1-x) = x*(1-x^2)/(1-x)^2. - Jaume Oliver Lafont, Mar 20 2009

a(n) = A000005(n) - A070824(n) for n >= 1.

E.g.f.: 2*exp(x) - x - 2. - Stefano Spezia, May 19 2024