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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..73.

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)

Formula

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

Example

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

Crossrefs

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

Sequence in context: A334592 A248756 A059942 * A046460 A327661 A117643

Adjacent sequences: A032447 A032448 A032449 * A032451 A032452 A032453

Keyword

nonn

Author

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

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

Status

approved