A332966 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.

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, 26, 26, 26, 26, 26, 33, 26, 29, 26, 31, 26, 37, 32, 26, 36, 26, 26, 33, 43, 26, 47, 30, 50, 26, 41, 53, 50, 26, 50, 50, 30, 50, 53, 57, 47, 37, 57, 26, 56, 65, 59

Offset

1,3

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

Rémy Sigrist, Scatterplot of the first 750000 terms

Formula

a(n) >= A003095(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 largest value 26, so a(42) = 26.

Prog

(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 }

Crossrefs

Cf. A003095, A248218, A330405, A332965.

Sequence in context: A123081 A020917 A308772 * A035643 A324925 A163946

Adjacent sequences: A332963 A332964 A332965 * A332967 A332968 A332969

Keyword

nonn

Author

Rémy Sigrist, Mar 04 2020

Status

approved