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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323017 T(n,k) = A321477(n,k)/A321476(n,k), 0 <= k <= n - 1. 0
 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 4, 2, 4, 2, 1, 2, 4, 2, 4, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS For Lucas sequences, say, rows in A172236, we are mainly concerned about the periods, ranks and the ratios of the periods to the ranks of them modulo a given integer n. The period of {A172236(k,m) modulo m} is given as A321477(n,k), and the rank, which is defined as the smallest l > 0 such that n divides A172236(k,l), is given as A321476(n,k). T(n,k) is their ratio, which is the multiplicative order of A172236(k,A321476(n,k)+1) modulo n. T(n,k) has value 1, 2 or 4. This is because A172236(k,m+1)^4 == 1 (mod A172236(k,m)). For n > 2, T(n,k) = 4 iff A321476(n,k) is odd; 1 iff A321476(n,k) is even but not divisible by 4; 2 iff A321476(n,k) is divisible by 4. See A172236 for some further properties. Let p be an odd prime. If p == 3 (mod 4), the p^e-th row consists of only 1 and 2; if p == 5 (mod 8), the p^e-th row consists of only 1 and 4. LINKS EXAMPLE Table begins   1,   1, 1,   1, 2, 2,   1, 1, 1, 1,   1, 4, 4, 4, 4,   1, 2, 2, 1, 2, 2,   1, 2, 1, 2, 2, 1, 2,   1, 2, 1, 2, 1, 2, 1, 2,   1, 2, 2, 1, 2, 2, 1, 2, 2,   1, 4, 2, 4, 2, 1, 2, 4, 2, 4,   ... PROG (PARI) A172236(k, m) = ([k, 1; 1, 0]^m)[2, 1] T(n, k) = my(i=1); while(A172236(k, i)%n!=0, i++); znorder(Mod(A172236(k, i+1), n)) CROSSREFS Cf. A172236, A321476, A321477. Sequence in context: A228528 A219244 A330231 * A273638 A277582 A037803 Adjacent sequences:  A323014 A323015 A323016 * A323018 A323019 A323020 KEYWORD nonn,tabl AUTHOR Jianing Song, Jan 07 2019 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 January 23 01:15 EST 2020. Contains 331166 sequences. (Running on oeis4.)