login
A106618
a(n) = numerator of n/(n+17).
4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 2, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 3, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 4, 69, 70, 71, 72, 73, 74
OFFSET
0,3
COMMENTS
a(n) <> n iff n = 17 * k, in this case, a(n) = k. - Bernard Schott, Feb 19 2019
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
Dirichlet g.f.: zeta(s-1)*(1 - 16/17^s). - R. J. Mathar, Apr 18 2011
a(n) = 2*a(n-17) - a(n-34). - G. C. Greubel, Feb 19 2019
From Amiram Eldar, Nov 25 2022: (Start)
Multiplicative with a(17^e) = 17^(e-1), and a(p^e) = p^e if p != 17.
Sum_{k=1..n} a(k) ~ (273/578) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 33*log(2)/17. - Amiram Eldar, Sep 08 2023
MAPLE
seq(numer(n/(n+17)), n=0..80); # Muniru A Asiru, Feb 19 2019
MATHEMATICA
f[n_]:=Numerator[n/(n+17)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
PROG
(Sage) [lcm(n, 17)/17 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009
(Magma) [Numerator(n/(n+17)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(100, n, n--; numerator(n/(n+17))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+17))); # Muniru A Asiru, Feb 19 2019
CROSSREFS
Cf. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).
Sequence in context: A357434 A309083 A375245 * A320113 A080684 A159062
KEYWORD
nonn,easy,frac,mult
AUTHOR
N. J. A. Sloane, May 15 2005
STATUS
approved