

A332965


a(n) is the number of distinct values in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.


2



1, 2, 3, 3, 3, 4, 4, 4, 5, 6, 6, 4, 4, 5, 5, 5, 8, 8, 6, 7, 4, 6, 8, 4, 4, 4, 5, 5, 11, 8, 5, 5, 6, 8, 6, 8, 6, 7, 6, 8, 7, 5, 8, 6, 5, 8, 14, 5, 9, 7, 8, 5, 9, 8, 10, 5, 6, 11, 11, 8, 15, 6, 6, 6, 12, 6, 12, 8, 8, 9, 18, 8, 9, 7, 5, 7, 6, 6, 8, 9, 11, 14, 11
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OFFSET

1,2


COMMENTS

For any n > 0, the sequence s is eventually periodic, so this sequence is well defined.
a(n) tends to infinity as n tends to infinity.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000


FORMULA

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


EXAMPLE

For n = 42:
 we have:
k s(k)
 
1 1
2 2
3 5
4 26
5 5
6 26
...
 the sequence s has 4 distinct values, so a(42) = 4.


PROG

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


CROSSREFS

Cf. A003095, A332966.
Sequence in context: A285761 A080405 A039728 * A334220 A234016 A029119
Adjacent sequences: A332962 A332963 A332964 * A332966 A332967 A332968


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Mar 04 2020


STATUS

approved



