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A276863
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First differences of the Beatty sequence A276854 for 1 + sqrt(5).
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4
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3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = floor(n*r) - floor(n*r - r), where r = 1 + sqrt(5), n >= 1.
a(n) = 1+floor(n*sqrt(5))-floor((n-1)*sqrt(5)). - Chai Wah Wu, Mar 16 2021
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MATHEMATICA
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z = 500; r = 1+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A276854 *)
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PROG
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(Python)
from sympy import integer_nthroot
def A276863(n): return 1+integer_nthroot(5*n**2, 2)[0]-integer_nthroot(5*(n-1)**2, 2)[0] # Chai Wah Wu, Mar 16 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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