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

Author

Rémy Sigrist, Mar 04 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Scatterplot of the first 750000 terms

Crossrefs

Cf. A003095, A248218, A330405, A332965.

Programs

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 }

Formula

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