A227109 Numerators of harmonic mean H(n, 5), n >= 0.

0, 5, 20, 15, 40, 5, 60, 35, 80, 45, 20, 55, 120, 65, 140, 15, 160, 85, 180, 95, 8, 105, 220, 115, 240, 25, 260, 135, 280, 145, 60, 155, 320, 165, 340, 35, 360, 185, 380, 195, 80, 205, 420, 215, 440, 9, 460, 235, 480, 245, 100, 255, 520, 265, 540, 55, 560

Offset: 0

Author

Wolfdieter Lang, Jul 01 2013

Keywords

• nonn
• frac
• easy

Comments

a(n) = numerator(H(n, 5)) = numerator(10*n/(n+5)), n>=0, with H(n, 5) the harmonic mean of n and 5.

The corresponding denominator is given in A227108(n), n>= 0.

a(n+5), n>=0, is the fifth column (m=5) of the triangle A227041.

Examples

			The rationals H(n,5) begin: 0, 5/3, 20/7, 15/4, 40/9, 5, 60/11, 35/6, 80/13, 45/7, 20/3, 55/8, 120/17, 65/9, ...
		

Crossrefs

Cf. A227041(n+5,5), A227108 (denominator).

Programs

Magma

[Numerator(10*n/(n+5)): n in [0..60]]; // Vincenzo Librandi, Nov 06 2016

Mathematica

Table[Numerator[(10 n / (n + 5))], {n, 0, 60}] (* Vincenzo Librandi, Nov 06 2016 *)

PARI

a(n) = numerator(10*n/(n+5)); \\ Michel Marcus, Nov 06 2016

Formula

a(n) = numerator(10*n/(n+5)), n >= 0.

a(n) = 10*n/gcd(n+5,10*n) = 10*n/gcd(n+5,50), n >= 0.