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A276863 First differences of the Beatty sequence A276854 for 1 + sqrt(5). 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, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = floor(n*r) - floor(n*r - r), where r = 1 + sqrt(5), n >= 1.
a(n) = A188187(n) + 3, as follows right from the definitions. - Michel Dekking, Sep 02 2019
a(n) = 1+floor(n*sqrt(5))-floor((n-1)*sqrt(5)). - Chai Wah Wu, Mar 16 2021
MATHEMATICA
z = 500; r = 1+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}]; (* A276854 *)
Differences[b] (* A276863 *)
PROG
(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
CROSSREFS
Sequence in context: A263998 A048181 A091799 * A227321 A309555 A262994
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Sep 24 2016
STATUS
approved

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Last modified July 15 07:28 EDT 2024. Contains 374324 sequences. (Running on oeis4.)