login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102460 a(n) = 1 if n is a Lucas number, else a(n) = 0. 14
0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The number of nonnegative integer solutions to 25*x^4-10*n^2*x^2+n^4-16=0. - Hieronymus Fischer, Jul 02 2007

a(n)=1 if and only if there is an integer m such that x=n is a root of p(x)=x^4-10*m^2*x^2+25*m^4-16. - Hieronymus Fischer, Jul 02 2007

For n>=3: a(n)=1 iff floor(log_phi(n+1/2))=ceiling(log_phi(n-1/2)). - Hieronymus Fischer, Jul 02 2007

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Casey Mongoven, Lucas Binary no. 1; electronic music created with this sequence.

Index entries for characteristic functions

FORMULA

G.f.: g(x)=sum{k>=0, x^A000032(k)}. - Hieronymus Fischer, Jul 02 2007

a(n)=1+floor(arcsinh(n/2)/log(phi))-ceiling(arccosh(n/2)/log(phi)) for n>=3, where phi=(1+sqrt(5))/2. - Hieronymus Fischer, Jul 02 2007

a(n)=1+A130241(n)-A130242(n) for n>=3. - Hieronymus Fischer, Jul 02 2007

a(n)=1+A130247(n)-A130242(n) for n=>2. - Hieronymus Fischer, Jul 02 2007

a(n)=A130245(n)-A130245(n-1) for n>=1. - Hieronymus Fischer, Jul 02 2007

For n>=3: a(n)=1 iff A130241(n)=A130242(n). - Hieronymus Fischer, Jul 02 2007

MATHEMATICA

{0}~Join~ReplacePart[ConstantArray[0, Last@ #], Map[# -> 1 &, #]] &@ Array[LucasL, 11, 0] (* Michael De Vlieger, Nov 22 2017 *)

PROG

(PARI) a(n)=my(f=factor(25*'x^4-10*n^2*'x^2+n^4-16)[, 1]); sum(i=1, #f, poldegree(f[i])==1 && polcoeff(f[i], 0)<=0) \\ Charles R Greathouse IV, Nov 06 2014

(PARI) A102460(n) = { my(u1=1, u2=3, old_u1); if(n<=2, sign(n), while(n>u2, old_u1=u1; u1=u2; u2=old_u1+u2); (u2==n)); }; \\ Antti Karttunen, Nov 22 2017

CROSSREFS

Cf. A000032, A130241, A130242, A130247, A123927.

Cf. partial sums A130245.

Cf. also A010056, A104162, A105348, A147612, A294878.

Sequence in context: A269528 A099859 A176416 * A080908 A131720 A131719

Adjacent sequences:  A102457 A102458 A102459 * A102461 A102462 A102463

KEYWORD

nonn

AUTHOR

Casey Mongoven, Apr 18 2005

EXTENSIONS

Data section extended up to a(123) by Antti Karttunen, Nov 22 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 06:34 EST 2019. Contains 329784 sequences. (Running on oeis4.)