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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 7 12:19 EST 2021. Contains 341885 sequences. (Running on oeis4.)