All integers from 1 to 73 are recorded in a sequence such that each number
-2
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All integers from 1 to 73 are recorded in a sequence such that each number (from the second onwards) divides the sum of all previous numbers.
What numbers can be in the third place and why?
The context is simple: I'm a math teacher and my student brought this task. But I can't solve it without coding. ((
sequences-and-series number-theory integers
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
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|
show 2 more comments
-2
$begingroup$
All integers from 1 to 73 are recorded in a sequence such that each number (from the second onwards) divides the sum of all previous numbers.
What numbers can be in the third place and why?
The context is simple: I'm a math teacher and my student brought this task. But I can't solve it without coding. ((
sequences-and-series number-theory integers
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
$endgroup$
1
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
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@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08
|
show 2 more comments
-2
-2
-2
1
$begingroup$
All integers from 1 to 73 are recorded in a sequence such that each number (from the second onwards) divides the sum of all previous numbers.
What numbers can be in the third place and why?
The context is simple: I'm a math teacher and my student brought this task. But I can't solve it without coding. ((
sequences-and-series number-theory integers
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
$endgroup$
All integers from 1 to 73 are recorded in a sequence such that each number (from the second onwards) divides the sum of all previous numbers.
What numbers can be in the third place and why?
The context is simple: I'm a math teacher and my student brought this task. But I can't solve it without coding. ((
sequences-and-series number-theory integers
sequences-and-series number-theory integers
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
edited Dec 30 '18 at 22:26
Joe Bradley
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
asked Dec 30 '18 at 21:52
Joe BradleyJoe Bradley
202
202
1
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
$begingroup$
@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08
|
show 2 more comments
1
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
$begingroup$
@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08
1
1
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
$begingroup$
@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08
|
show 2 more comments
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1
$begingroup$
Have you tried with smaller odd numbers/primes to see if you can spot any pattern. What happens with $5$? With $7$?
$endgroup$
– Mark Bennet
Dec 30 '18 at 23:14
$begingroup$
@Mark Bennet Thank for supporting me. ) Unfortunately, the situation for 9, 13, 15, 20+ and other sequence lengths is different. (
$endgroup$
– Joe Bradley
Dec 30 '18 at 23:33
$begingroup$
@JoeBradley Are you sure such a sequence exists? Which Math Olympia had this as a problem? They usually publish their solutions.
$endgroup$
– John Douma
Dec 31 '18 at 0:00
$begingroup$
@john-douma I would be glad if this task had been given at any concrete competition. ) Тhis is the final task of one of the training test to prepare for the USE in Russia. The complexity of this task traditionally corresponds to the level of a good math Olympiad. If you like I can provide a link to this test (in Russian of course). There's only answer there, no solution.
$endgroup$
– Joe Bradley
Dec 31 '18 at 8:19
$begingroup$
Comments are not for extended discussion; this conversation has been moved to chat.
$endgroup$
– quid♦
Jan 1 at 2:08