A352641 - OEIS

%I #9 Mar 29 2022 16:39:06

%S 0,5,6,42,8,69,42,92,252,159,120,164,462,472,305,713,118,2073,495,99,

%T 172,419,2189,305,518,970,601,1174,1007,1209,6202,331,2928,499,2118,

%U 416,3621,3921,302,3042,50,25744,5079,1882,5535,2216,1492,4845,274,889,1571

%N For any n > 0, let E_n be the variant of Van Eck's sequence where values are taken mod n; if E_n is eventually periodic, then a(n) is the length of its transient part; otherwise a(n) = -1.

%C For any n > 0: E_n(1) = 0, and for any k > 0, if E_n(m) = E_n(k) for some m < k, take the largest such m and set E_n(k+1) = (k-m) mod n; otherwise E_n(k+1) = 0.

%C Note that in general, E_n(k) <> A181391(k) mod n.

%C For n <= 10000:

%C - E_n is always eventually periodic,

%C - except for n = 1, 3 and 4, E_n is eventually constant (with value 1).

%C Is E_n eventually periodic for all n?

%H Rémy Sigrist, <a href="/A352641/a352641.txt">C program</a>

%e For n = 3:

%e - E_3 is eventually 7-periodic:

%e           0 0 1 0 2 0 (2 2 1 0 1 2 1)*

%e - the transient part has 6 terms,

%e - so a(3) = 6.

%o (C) See Links section.

%Y Cf. A181391.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Mar 25 2022