login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A237835 a(n) = n*(Pisano period of n) divided by (Pisano period of n^2). 4
1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 4, 3, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 2, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 12, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Arpan Saha and C. S. Karthik, A few equivalences of Wall-Sun-Sun prime conjecture, arXiv:1102.1636 [math.NT], 2011.

Eric Weisstein's World of Mathematics, Pisano period.

Wikipedia, Pisano period.

FORMULA

a(n) = n/A237517(n).

MATHEMATICA

pp[1] = 1; pp[n_] := For[k = 1, True, k++, If[Mod[Fibonacci[k], n] == 0 && Mod[Fibonacci[k+1], n] == 1, Return[k]]];

a[n_] := n pp[n]/pp[n^2];

Array[a, 100] (* Jean-Fran├žois Alcover, Dec 06 2018 *)

PROG

(PARI) fibmod(n, m)=((Mod([1, 1; 1, 0], m))^n)[1, 2]

entry_p(p)=my(k=1, c=Mod(1, p), o); while(c, [o, c]=[c, c+o]; k++); k

entry(n)=if(n==1, return(1)); my(f=factor(n), v); v=vector(#f~, i, if(f[i, 1]>1e14, entry_p(f[i, 1]^f[i, 2]), entry_p(f[i, 1])*f[i, 1]^(f[i, 2] - 1))); if(f[1, 1]==2&&f[1, 2]>1, v[1]=3<<max(f[1, 2]-2, 1)); lcm(v)

per(n)=if(n==1, return(1)); my(k=entry(n)); forstep(i=k, n^2, k, if(fibmod(i-1, n)==1, return(i)))

a(n)=n*per(n)/per(n^2)

CROSSREFS

Cf. A237517, A001175, A001176.

Sequence in context: A323160 A323166 A007732 * A126795 A334491 A276997

Adjacent sequences:  A237832 A237833 A237834 * A237836 A237837 A237838

KEYWORD

nonn

AUTHOR

Charles R Greathouse IV, Feb 13 2014

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 November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)