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 A248219 Indices where A248218(n) = 1. 12

%I

%S 1,3,7,19,21,31,37,43,57,93,111,129,133,157,217,259,301,307,313,399,

%T 463,471,499,589,613,651,703,777,817,903,921,939,967,1099,1147,1333,

%U 1389,1497,1591,1767,1839,2109,2149,2191,2451,2683,2901,2983,3241,3297,3441

%N Indices where A248218(n) = 1.

%C n is in the sequence if there exists a number k0 such that A003095(k) mod n = A003095(k0) mod n for all k >= k0.

%C Conjecture: a(n) ~ n^2.

%H Vaclav Kotesovec, <a href="/A248219/b248219.txt">Table of n, a(n) for n = 1..717</a>

%e 7 is in the sequence since A003095 mod 7 is {1, 2, 5, 5, 5, 5, ...}, k0 = 3, A003095(k) mod 7 = 5 for all k >= k0. The period is 1.

%e 10 is not in the sequence since A003095 mod 10 is {1, 2, 5, 6, 7, 0, 1, 2, 5, 6, 7, 0, 1, 2, ...} and the period is 6, not 1.

%t nmax=10000; periods=Table[m=Rest[NestList[Mod[#^2+1,n]&,0,nmax]]; period=0; j=1; While[j<=Length[m]&&period==0,If[m[[Length[m]-j]]==m[[Length[m]]],period=j]; j++]; period,{n,1,nmax}]; Select[Range[nmax],periods[[#]]==1&]

%Y Cf. A003095, A247981, A248218.

%K nonn

%O 1,2

%A _Vaclav Kotesovec_, Oct 04 2014

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Last modified July 17 03:18 EDT 2019. Contains 325092 sequences. (Running on oeis4.)