A332966 - OEIS

%I #13 Nov 10 2020 15:40:34

%S 0,1,2,2,2,5,5,5,8,7,6,5,5,12,11,10,16,17,12,17,5,17,13,5,5,5,26,26,

%T 26,26,26,26,26,33,26,29,26,31,26,37,32,26,36,26,26,33,43,26,47,30,50,

%U 26,41,53,50,26,50,50,30,50,53,57,47,37,57,26,56,65,59

%N a(n) is the largest value in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.

%C For any n > 0, the sequence s is eventually periodic, so this sequence is well defined.

%C a(n) tends to infinity as n tends to infinity.

%H Rémy Sigrist, <a href="/A332966/b332966.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A332966/a332966.png">Scatterplot of the first 750000 terms</a>

%F a(n) >= A003095(k) for any k >=0 and n > A003095(k).

%e For n = 42:

%e - we have:

%e   k  s(k)

%e   -  ----

%e   1     1

%e   2     2

%e   3     5

%e   4    26

%e   5     5

%e   6    26

%e   ...

%e - the sequence s has largest value 26, so a(42) = 26.

%o (PARI) a(n) = { my (s=0, v=s, w=0); while (!bittest(w,s), w+=2^s; v=max(v,s); s=(s^2+1)%n); v }

%Y Cf. A003095, A248218, A330405, A332965.

%K nonn

%O 1,3

%A _Rémy Sigrist_, Mar 04 2020