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A293323
Least integer k such that k/2^n > 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.
3
1, 2, 3, 5, 10, 20, 40, 80, 159, 317, 633, 1266, 2532, 5063, 10126, 20252, 40504, 81007, 162014, 324028, 648056, 1296112, 2592223, 5184445, 10368890, 20737780, 41475559, 82951118, 165902236, 331804472, 663608943, 1327217885, 2654435770, 5308871539
OFFSET
0,2
LINKS
FORMULA
a(n) = ceiling(r*2^n), where r = (-1+sqrt(5))/2.
a(n) = A293322(n) + 1.
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 *)
PROG
(PARI) a(n) = ceil(2^(n-1)*(sqrt(5)-1)); \\ Altug Alkan, Oct 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 07 2017
STATUS
approved