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A293321
The integer k that minimizes |k/2^n - tau^2|, where tau = (1+sqrt(5))/2 = golden ratio.
3
3, 5, 10, 21, 42, 84, 168, 335, 670, 1340, 2681, 5362, 10723, 21447, 42894, 85788, 171575, 343151, 686302, 1372604, 2745208, 5490415, 10980830, 21961661, 43923322, 87846643, 175693287, 351386574, 702773148, 1405546295, 2811092590, 5622185181, 11244370361
OFFSET
0,1
LINKS
FORMULA
a(n) = floor(1/2 + r*2^n), where r = (3+sqrt(5))/2.
a(n) = A293319(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293316(n).
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
(PARI) a(n) = (2^n*(3+sqrt(5))+1)\2; \\ Altug Alkan, Oct 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2017
STATUS
approved