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

0,3

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

Table of n, a(n) for n=0..97.

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 W. Weisstein, MathWorld -- Waring's Problem.

Index entries for linear recurrences with constant coefficients, signature (1).

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.

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 *)

Prog

(PARI) a(n)=min(n, 2) \\ Charles R Greathouse IV, Jun 01 2011
(Haskell)
a130130 = min 2
a130130_list = 0 : 1 : repeat 2  -- Reinhard Zumkeller, Jun 27 2013

Crossrefs

Cf. A158411. - Jaume Oliver Lafont, Mar 20 2009

Sequence in context: A065685 A084100 A329683 * A046698 A211662 A007395

Adjacent sequences: A130127 A130128 A130129 * A130131 A130132 A130133

Keyword

nonn,easy,changed

Author

Paul Curtz, Aug 01 2007

Status

approved