A real HOTPO-tato

Number Theory Level 1

Define the operation "HOTPO" as follows, for positive integers.

If n is odd and greater than 1, form 3n+1

If n is even, form n/2

If n = 1, terminate the process

Example:

It takes 5 operations for HOTPO (5) to terminate.

HOTPO (5) = 16

HOTPO (16) = 8

HOTPO (8) = 4

HOTPO (4) = 2

HOTPO (2) = 1 (stop)

How many operations does it take for HOTPO(17) to terminate?


The answer is 12.

Denton Young by Denton Young , 47, USA

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4 solutions

Denton Young
Aug 20, 2015

HOTPO (17) = 52

HOTPO (52) = 26

HOTPO (26) = 13

HOTPO (13) = 40

HOTPO (40) = 20

HOTPO (20) = 10

HOTPO (10) = 5

HOTPO (5) = 16

HOTPO (16) = 8

HOTPO (8) = 4

HOTPO (4) = 2

HOTPO ( 2) = 1 (stop)

Try tracking HOTPO (27). Bring a good-sized sheet of paper.

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Edwin Gray
Sep 8, 2018

We should have called the function Collatz, after Luther Collatz who first conjectured that the defined sequence will always terminate at 1.(1937). For those looking for something to do, it is still an open question. Ed Gray

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Chew-Seong Cheong
Aug 23, 2015

I have written an Excel spreadsheet to solve it. H O T P O ( 17 ) = 12 HOTPO(17)=12 and H O T P O ( 27 ) = 111 HOTPO(27) = 111 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused 
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hotpo = 17

ctr = 0
while hotpo != 1:
    if hotpo % 2:
        hotpo = hotpo*3 + 1
        ctr += 1
    else:
        hotpo /= 2
        ctr += 1

print ctr

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