A359803 - OEIS

A359803

a(1) = 1; for n > 1, a(n) = n-1 if a(n-1) = 1, otherwise, apply the '3x+1' function to a(n-1)

1, 1, 2, 1, 4, 2, 1, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 24, 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, 35, 106, 53, 160, 80, 40, 20, 10, 5, 16, 8, 4, 2, 1, 49, 148, 74, 37, 112, 56, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..71.

EXAMPLE

For n = 5, the sequence so far is (1, 1, 2, 1) a(4) = 1, therefore a(5) = 5-1 = 4.

For n = 6, the sequence so far is (1, 1, 2, 1, 4), 4 is not 1, so we apply the '3x+1' function, 4 is even, so we divide it by 2, therefore a(6) = 4/2 = 2.

For n = 9, the sequence so far is (1, 1, 2, 1, 4, 2, 1, 7), 7 is not 1, so we apply the '3x+1' function, 7 is odd, so we multiply it by 3 and add 1, therefore a(9) = 3*(7)+1 = 22.

PROG

(Python)

def a(length):

sequence = [1]

while len(sequence) < length:

last_term = sequence[-1]

if last_term == 1:

next_term = len(sequence)

elif last_term % 2 == 0:

next_term = last_term // 2

else:

next_term = 3 * last_term + 1