A152077 Length of the trajectory of the map x->A003132(x) started at x=n^2 up to the end of its first period.

1, 8, 12, 8, 11, 16, 5, 12, 11, 2, 18, 13, 17, 17, 13, 11, 11, 11, 13, 9, 13, 14, 11, 11, 11, 19, 12, 5, 12, 12, 17, 14, 15, 17, 13, 14, 17, 6, 4, 9, 14, 14, 16, 17, 13, 9, 9, 11, 14, 11, 15, 14, 11, 14, 11, 14, 11, 7, 13, 16, 17, 12, 15, 7, 6, 4, 18, 15, 14, 5, 9, 10, 12, 16, 13, 15, 12, 12

Offset: 1

Author

R. J. Mathar, Sep 16 2009

Keywords

• nonn
• base

Comments

This accumulates the length of the "transient" or "pre-periodic" part of the trajectory started at n^2 plus the length of the first period.

Examples

			a(5)=11 since the trajectory starting at x=5^2 is 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58 the next term 89 is already there.
a(10)= 2 since the trajectory starting at x=10^2 is 100,1 and the next term is again the 1.
a(11)= 18 because the trajectory is 121, 6, 36, 45, 41, 17, 50, 25, 29, 85, 89, 145, 42, 20, 4, 16, 37, 58, the next 89 is already there.
		

Crossrefs

Cf. A031176, A160862.

Formula

a(n) = A099645(n^2)+A031176(n^2) .