A066745 Least number of applications of f(k) = k(k+1)+1 to n to yield a prime, if this number exists; -1 otherwise.

2, 1, 0, 0, 2, 0, 1, 0, 1, 3, 2, 0, 1, 0, 1, 1

Offset

0,1

Comments

a(16) >= 18 (unless a(16) = -1). - Pontus von Brömssen, Apr 22 2023

Links

Table of n, a(n) for n=0..15.

Formula

From Pontus von Brömssen, Apr 22 2023: (Start)

a(n) = 0 if n is prime, otherwise a(n) = 1 + a(n*(n+1)+1) (unless a(n) = -1).

a(n) is even if and only if (a) n = 0, (b) n is prime, or (c) n == 1 (mod 3), n >= 4, and a(n) != -1. This can be seen by considering how f maps the residue classes modulo 3: 2 -> 1 -> 0 -> 1.

(End)

Example

f(f(f(9))) = f(f(91)) = f(8373) = 70115503, a prime, whereas 9, 91, 8373 are composite; so a(9) = 3.

Mathematica

Table[Length[NestWhileList[#(#+1)+1&, n, !PrimeQ[#]&, 1, 20]]-1, {n, 0, 15}] (* Arbitrary maximum of 20 iterations of the function set. *) (* Harvey P. Dale, Apr 19 2023 *)

Crossrefs

Sequence in context: A335021 A176202 A040081 * A239393 A256637 A113063

Adjacent sequences: A066742 A066743 A066744 * A066746 A066747 A066748

Keyword

nonn,more

Author

Joseph L. Pe, Jan 16 2002

Extensions

a(0) prepended by Pontus von Brömssen, Apr 22 2023

Status

approved