A326825 a(n) is the number of iterations needed to reach 1 or 5 starting at n and using the map k -> (k/2 if k is even, otherwise k + (smallest triangular number > k)). Set a(n) = -1 if the trajectory never reaches 1 or 5.

0, 1, 6, 2, 0, 7, 7, 3, 5, 1, 12, 8, 10, 8, 8, 4, 6, 6, 4, 2, 15, 13, 58, 9, 56, 11, 52, 9, 36, 9, 15, 5, 28, 7, 13, 7, 20, 5, 18, 3, 18, 16, 16, 14, 59, 59, 59, 10, 14, 57, 57, 12, 55, 53, 51, 10, 22, 37, 55, 10, 24, 16, 22, 6, 35, 29, 14, 8, 27, 14, 12, 8, 10, 21, 23, 6, 27, 19

Offset

1,3

Comments

It is conjectured that this algorithm will always terminate at 1 or 5.

Jim Nastos verified the conjecture for n <= 354999.

The conjecture holds for all n <= 10^9. - Jon E. Schoenfield, Oct 20 2019

Links

Table of n, a(n) for n=1..78.

Formula

For n = 11: 11+15=26; 26/2=13; 13+15=28; 28/2=14; 14/2=7; 7+10=17; 17+21=38; 38/2=19; 19+21=40; 40/2=20; 20/2=10; 10/2=5; taking 12 steps to reach 5, so a(11)=12.

Crossrefs

Cf. A006577, A326823.

Sequence in context: A248680 A021621 A197844 * A182639 A244135 A120002

Adjacent sequences: A326822 A326823 A326824 * A326826 A326827 A326828

Keyword

nonn

Author

Ali Sada, Oct 20 2019

Extensions

Edited by Jon E. Schoenfield and N. J. A. Sloane, Oct 20 2019

Status

approved