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A293324
The integer k that minimizes |k/2^n - 1/tau|, where tau = (1+sqrt(5))/2 = golden ratio.
3
1, 1, 2, 5, 10, 20, 40, 79, 158, 316, 633, 1266, 2531, 5063, 10126, 20252, 40503, 81007, 162014, 324028, 648056, 1296111, 2592222, 5184445, 10368890, 20737779, 41475559, 82951118, 165902236, 331804471, 663608942, 1327217885, 2654435769, 5308871539
OFFSET
0,3
LINKS
FORMULA
a(n) = floor(1/2 + r*2^n), where r = (-1+sqrt(5))/2.
a(n) = A293322(n) if (fractional part of r*2^n) < 1/2, else a(n) = A293323(n).
MATHEMATICA
z = 120; r = -1+GoldenRatio;
Table[Floor[r*2^n], {n, 0, z}]; (* A293322 *)
Table[Ceiling[r*2^n], {n, 0, z}]; (* A293323 *)
Table[Round[r*2^n], {n, 0, z}]; (* A293324 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2017
STATUS
approved