A047203 Numbers that are congruent to {0, 2, 3, 4} mod 5.

0, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 87, 88, 89

Offset

1,2

Comments

Complement of A016861. - Reinhard Zumkeller, Oct 23 2006

Links

Table of n, a(n) for n=1..72.

Melvyn B. Nathanson, On the fractional parts of roots of positive real numbers, Amer. Math. Monthly, Vol. 120, No. 5 (2013), pp. 409-429 [see p. 417].

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

A027445(a(n)) mod 10 = 0. - Reinhard Zumkeller, Oct 23 2006

a(n) = floor((5n-2)/4). - Gary Detlefs, Mar 06 2010

a(n) = floor((15n-5)/12). - Gary Detlefs, Mar 07 2010

G.f.: x^2*(2+x+x^2+x^3)/((1+x)*(1+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, May 14 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (10*n-7+(-1)^n+2*(-1)^((2*n+3+(-1)^n)/4))/8.

a(2n) = A047211(n), a(2n-1) = A047218(n).

a(n) = A047207(n+1) - 1.

a(n+2) = n + 2 + A002265(n) for n>0.

a(n+3)-a(n+2) = A177704(n) for n>0.

a(1-n) = - A001068(n). (End)

Sum_{n>=2} (-1)^n/a(n) = log(5)/4 + sqrt(5)*log(phi)/10 - sqrt(5-2*sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021

Maple

seq(floor(5*n-2)/4), n=1..72); # Gary Detlefs, Mar 06 2010
seq(floor((15*n-5)/12), n=1..72); # Gary Detlefs, Mar 07 2010

Mathematica

Flatten[Table[5*n + {0, 2, 3, 4}, {n, 0, 20}]] (* T. D. Noe, Nov 12 2013 *)

Prog

(PARI) a(n)=(5*n-2)\4 \\ Charles R Greathouse IV, Jun 11 2015
(Magma) [Floor((5*n-2)/4) : n in [1..100]]; // Wesley Ivan Hurt, May 14 2016

Crossrefs

Cf. A001068, A001622, A002265, A016861, A027445, A047207, A047211, A047218, A177704.

Sequence in context: A226066 A005838 A184486 * A080919 A267303 A267307

Adjacent sequences: A047200 A047201 A047202 * A047204 A047205 A047206

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Reinhard Zumkeller, Oct 23 2006

Status

approved