The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A247523

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A247523

Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
(history; published version)

#16 by Joerg Arndt at Sat May 05 08:14:46 EDT 2018

FORMULA

a(n) = n*round(cos(2^(n-2)*Pi*(1/phi^2))^2) where phi = (1 + sqrt(5))/2 - golden ratio. - Aivaras Stankaitis, May 05 2018

or

x(1)=sin(Pi*(1/phi^2)/2)^2

x(n+1)=4*X(n)*(1-X(n))

a(n)=n*(1-round(x(n)))

KEYWORD

nonn,easy,base,changed

STATUS

editing

approved

#15 by Aivaras Stankaitis at Sat May 05 07:22:00 EDT 2018

FORMULA

a(n)=n*(1-round(x(n)))

Discussion

Sat May 05

08:14

Joerg Arndt: So, indeed incorrect.  I'll revert this edit.

#14 by Aivaras Stankaitis at Sat May 05 07:17:55 EDT 2018

FORMULA

or

x(1)=sin(Pi*(1/phi^2)/2)^2

x(n+1)=4*X(n)*(1-X(n))

a(n)=n*(1-round(x(n))

#13 by Joerg Arndt at Sat May 05 06:42:04 EDT 2018

STATUS

proposed

editing

Discussion

Sat May 05

06:45

Aivaras Stankaitis: Described formula generating integer sequence a(1)=1, a(2)=0, a(3)=3, a(4)=0, a(5)=5, a(6)=6, a(7)=7, a(8)=0, a(9)=9, a(10)=10, a(11)=0, ...

#12 by Omar E. Pol at Sat May 05 06:02:41 EDT 2018

STATUS

editing

proposed

Discussion

Sat May 05

06:42

Joerg Arndt: Formula gives 1, 0, 3, 0, 5, 6, 7, 0, 9, 10, 0, 12, 0, 0, 15, 16, 0, 0, 19, 20, 21, 0, ...

#11 by Omar E. Pol at Sat May 05 06:02:14 EDT 2018

FORMULA

a(n) = n*round(cos(2^(n-2)*Pi*(1/phi^2))^2) where phi = (1 + sqrt(5))/2 - golden ratio. - _Aivaras Stankaitis _, May 05 2018

STATUS

proposed

editing

Discussion

Sat May 05

06:02

Omar E. Pol: Corrected attribution format.

#10 by Aivaras Stankaitis at Sat May 05 05:36:18 EDT 2018

STATUS

editing

proposed

#9 by Aivaras Stankaitis at Sat May 05 05:36:11 EDT 2018

FORMULA

a(n)=n*round(cos(2^(n-2)*Pi*(1/phi^2))^2) where phi=(1 + sqrt(5))/2 - golden ratio.- Aivaras Stankaitis May 05 2018

STATUS

approved

editing

#8 by N. J. A. Sloane at Fri Sep 26 21:12:26 EDT 2014

STATUS

proposed

approved

#7 by Clark Kimberling at Fri Sep 26 18:06:08 EDT 2014

STATUS

editing

proposed