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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A248218 Period in residues modulo n in iteration of x^2 + 1 starting at 0. 16
 1, 2, 1, 2, 3, 2, 1, 2, 3, 6, 2, 2, 4, 2, 3, 2, 6, 6, 1, 6, 1, 2, 2, 2, 3, 4, 3, 2, 2, 6, 1, 2, 2, 6, 3, 6, 1, 2, 4, 6, 7, 2, 1, 2, 3, 2, 4, 2, 6, 6, 6, 4, 2, 6, 6, 2, 1, 2, 3, 6, 10, 2, 3, 2, 12, 2, 2, 6, 2, 6, 11, 6, 6, 2, 3, 2, 2, 4, 4, 6, 9, 14, 5, 2, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is a period in the sequence A003095 modulo n. For n <= 10000 is the maximal period a(7921) = 1232. For n <= 100000 is the maximal period a(73205) = 7260. For n <= 500000 is the maximal period a(357911) = 54670. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..100000 FORMULA a(LCM(i,j)) = LCM(a(i),a(j)). - Robert Israel, Mar 08 2021 EXAMPLE n=5, residues are 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, ... , period is 3, a(5)=3. n=7, residues are 1, 2, 5, 5, 5, 5, 5, ... , final period is 1, therefore a(7)=1. n=10, residues are 1, 2, 5, 6, 7, 0, 1, 2, 5, 6, 7, 0, 1, 2, ... , a(10)=6. n=43, residues are 1, 2, 5, 26, 32, 36, 7, 7, 7, 7, ... , a(43) = 1. n=229, residues are 1, 2, 5, 26, 219, 101, 126, 76, 52, 186, 18, 96, 57, 44, 105, 34, 12, 145, 187, 162, 139, 86, 69, 182, 149, 218, 122, 0, 1, 2, 5, 26, 219, 101, 126, 76, 52, 186, 18, 96, 57, 44, 105, 34, 12, 145, 187, 162, 139, 86, 69, 182, 149, 218, 122, 0, 1, 2, 5, 26, ... , period is 28, a(229)=28. This program is for experiments (n<100): Rest[NestList[Mod[#^2+1, n] &, 0, 100]] MATHEMATICA Table[m=Rest[NestList[Mod[#^2+1, n]&, 0, 1000]]; period=0; j=1; While[j<=Length[m] && period==0, If[m[[Length[m]-j]]==m[[Length[m]]], period=j]; j++]; period, {n, 1, 1000}] PROG (PARI) A248218(m, t=0, u=[t])=until(#Set(u=concat(u, t=(t^2+1)%m))<#u, ); for(i=1, #u, t==u[#u-i]&&return(i)) \\ M. F. Hasler, Mar 25 2015 CROSSREFS Cf. A248219, A256342 - A256349, A003095, A247981, A001175. Sequence in context: A008342 A277214 A278603 * A182110 A175328 A338776 Adjacent sequences:  A248215 A248216 A248217 * A248219 A248220 A248221 KEYWORD nonn AUTHOR Vaclav Kotesovec, Oct 04 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.

Last modified May 6 15:22 EDT 2021. Contains 343586 sequences. (Running on oeis4.)