login
A293320
Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.
3
3, 6, 11, 21, 42, 84, 168, 336, 671, 1341, 2681, 5362, 10724, 21447, 42894, 85788, 171576, 343151, 686302, 1372604, 2745208, 5490416, 10980831, 21961661, 43923322, 87846644, 175693287, 351386574, 702773148, 1405546296, 2811092591, 5622185181, 11244370362
OFFSET
0,1
LINKS
FORMULA
a(n) = ceiling(r*2^n), where r = (3+sqrt(5))/2.
a(n) = A293319(n) + 1.
MATHEMATICA
z = 120; r = 1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}]; (* A293319 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293320 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293321 *)
PROG
(Magma) [Ceiling((2^n*(3+Sqrt(5)))/2): n in [0..33]]; // Vincenzo Librandi, Oct 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2017
STATUS
approved