

A349877


a(n) is the number of times the map x > A353314(x) needs to be applied to n to reach a multiple of 3, or 1 if the trajectory never reaches a multiple of 3.


5



0, 2, 14, 0, 1, 13, 0, 4, 1, 0, 12, 3, 0, 1, 3, 0, 4, 1, 0, 11, 2, 0, 1, 2, 0, 2, 1, 0, 2, 3, 0, 1, 3, 0, 10, 1, 0, 4, 5, 0, 1, 7, 0, 3, 1, 0, 3, 2, 0, 1, 2, 0, 2, 1, 0, 2, 4, 0, 1, 9, 0, 3, 1, 0, 3, 4, 0, 1, 5, 0, 6, 1, 0, 4, 2, 0, 1, 2, 0, 2, 1, 0, 2, 7, 0, 1, 4, 0, 6, 1, 0, 6, 3, 0, 1, 3, 0, 5, 1, 0, 8, 2, 0
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OFFSET

0,2


COMMENTS

Equally, number of iterations of A353313 needed to reach a multiple of 3, or 1 if no multiple of 3 is ever reached.  Antti Karttunen, Apr 14 2022


LINKS



FORMULA

(End)


EXAMPLE

a(1) = 2 : 1 > 4 > 9 (as it takes two applications of A353314 to reach a multiple of three),
a(2) = 14 : 2 > 5 > 10 > 19 > 34 > 59 > 100 > 169 > 284 > 475 > 794 > 1325 > 2210 > 3685 > 6144
a(3) = 0 : 3 (as the starting point 3 is already a multiple of 3).
a(4) = 1 : 4 > 9
a(7) = 4 : 7 > 14 > 25 > 44 > 75.


PROG

(Python)
import itertools
def f(n):
for i in itertools.count():
quot, rem = divmod(n, 3)
if rem == 0:
return i
n = (5 * quot) + rem + 3
(PARI)
A353314(n) = { my(r=(n%3)); if(!r, n, ((5*((nr)/3)) + r + 3)); };


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



