A059536 - OEIS

%I #23 Jul 07 2024 01:42:36

%S 2,5,7,10,12,15,17,20,22,25,28,30,33,35,38,40,43,45,48,51,53,56,58,61,

%T 63,66,68,71,73,76,79,81,84,86,89,91,94,96,99,102,104,107,109,112,114,

%U 117,119,122,124,127,130,132,135,137,140,142,145,147,150,153,155,158

%N Beatty sequence for zeta(2)/(zeta(2)-1).

%H Harry J. Smith, <a href="/A059536/b059536.txt">Table of n, a(n) for n = 1..2000</a>

%H Aviezri S. Fraenkel, Jonathan Levitt and Michael Shimshoni, <a href="http://dx.doi.org/10.1016/0012-365X(72)90012-X">Characterization of the set of values f(n)=[n alpha], n=1,2,...</a>, Discrete Math. 2 (1972), no.4, 335-345.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>.

%F a(n) = floor(n*zeta(2)/(zeta(2)-1)). - _Michel Marcus_, Jan 05 2015

%t Floor[Range[100]*Zeta[2]/(Zeta[2] - 1)] (* _Paolo Xausa_, Jul 06 2024 *)

%o (PARI) { default(realprecision, 100); b=zeta(2)/(zeta(2) - 1); for (n = 1, 2000, write("b059536.txt", n, " ", floor(n*b)); ) } \\ _Harry J. Smith_, Jun 27 2009

%Y Cf. A013661. Beatty complement is A059535.

%K nonn,easy

%O 1,1

%A _Mitch Harris_, Jan 22 2001