A032450 Period of finite sequence g(n) related to Poulet's Conjecture.

1, 3, 2, 2, 3, 7, 6, 12, 4, 2, 3, 12, 4, 7, 6, 4, 7, 6, 12, 15, 8, 12, 28, 6, 12, 4, 7, 12, 4, 7, 6, 28, 12, 6, 12, 4, 7, 8, 15, 8, 15, 31, 30, 72, 24, 60, 16, 6, 12, 4, 7, 24, 60, 16, 31, 30, 72, 8, 15, 12, 28, 16, 31, 30, 72, 24, 60, 12, 28, 8, 15, 60, 16

Offset: 1

Author

Ursula Gagelmann (gagelmann(AT)altavista.net), Apr 07 1998

Keywords

• nonn

Comments

Poulet's Conjecture states that for any integer n, the sequence f_0(n) = n, f_2k+1(n)=sigma(f_2k(n)), f_2k(n)=phi(f_2k-1(n)) (where sigma = A000203 and phi = A000010) is eventually periodic.

Examples

			Poulet's sequence starting at 1 is 1->1->1->.. which contributes [1]. Starting at 2: 2->3->2->3->.. which contributes [3,2]. Starting at 3: 3->4->2->3->2->3... which contributes [2,3]. Starting at 4: 4->7->6->12->4->7->6->12.. which contributes  [7, 6, 12, 4]. - _R. J. Mathar_, May 08 2020
		

References

• P. Poulet, Nouvelles suites arithmétiques, Sphinx vol. 2 (1932) pp. 53-54.

Links

• Leon Alaoglu and Paul Erdős, A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), 881-882.
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000010, A000203, A001229, A036845, A095955, A096865.

Formula

g(1)=n; thereafter g(2k)=sigma(g(2k-1)), g(2k+1)=phi(g(2k)).

Extensions

Revised definition and added formula from Ursula Gagelmann, Apr 07 1998 - N. J. A. Sloane, May 08 2020

Missing a(42)=31 inserted and more terms from Sean A. Irvine, Jun 21 2020