Primax - International Math Competition

 The editors of Acta Mundi and the Changing World announce an international mathematics competition

PRIMAX

according to the following conditions.

1. The purpose of the competition is to find functions that give prime numbers in a maximum number. In the use of the term in this competition, a function is a closed arithmetic formula with one variable interpreted on the natural numbers.

2. Anyone may enter the competition by sending an e-mail to primax@valtozovilag.hu with the formula of the function and any other information necessary to participate until the end of November of the current year. Participation in the competition requires a net payment of 1001 HUF to the editorial bank account.

3. It is irrelevant whether the subject formula is original or already known in mathematics. At the same time, it will be appreciated if the participant indicates the origin of the existing formula.

4. The winner of the competition is the one who submits the formula that produces the highest number of prime numbers. The evaluation is done in two categories.

A. Total result: the number of prime numbers in the first 100 values. In case of equality, we take into account the number of prime numbers between the first 200 values, etc.

B. Initial result: counts the number of consecutive prime numbers starting from the first value.

5. The winners of the competition will receive a diploma and a cash reward equal to 80% of the participation fees and sponsors' donations. If in one year there is no better result than the previous year, the new contributions will increase the reward for next year.

6. Winners of both categories will be announced separately, their rewards are equal. If several participants submit the same formula, the first one who submitted the formula correctly will be considered the winner.

7. The date of the announcement of the results is December 13 of the current year, the first opportunity on December 13, 2019.

8. Applicants must agree that the resulting sequence of the winning formula will be added to the OEIS, if it is not part of it, otherwise the editors will be allowed to submit it.

9. Only international and Hungarian laws will be applicable to the competition.

Budapest, September 20, 2019

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One interesting sequence

 

1, 2, 1, 3, 2, 4, 5, 3, 6, 7, 4, 10, 8, 12, 12, 13, 4, 16, 17, 3, 18, 19, 4, 22, 14, 19, 8, 26, 16, 28, 24, 29, 4, 32, 33, 25, 32, 36, 36, 37, 4, 40, 38, 25, 40, 41, 6, 45, 44, 39, 38, 33, 42, 47, 8, 54, 54, 55, 48, 57, 42, 55, 52, 51, 48, 63, 60, 63, 62, 39…

The sequence’s formula is a(1)=1, a(2)=2, for n>2 a(n)=n-largest prime which divides a(n-1). For “the largest prime which divides n we can use the LPD(n) notation.

For example, let n=6. a(5)=2. Largest prime, which divides 2, is 2. So a(6)=6-2=4.

Is this sequence interesting?

Everyone has the right to his own opinion, and therefore no one is responsible.

I thing that this sequence is very interesting because a(n)=n-LPD(a(n-1)), and no a(n)=n-LPD(n-1). In the latter case, we obtain a similar but less exciting sequence. Because of this peculiarity, I would call the original sequence a “kalach” sequence.

One first observation: if n is a prime then a(n) is often even, but there is at least one exception: a(19) = 17.  Conversely, it appears that if a(n) is a prime, then n is even.

According to my intention, I will report on other interesting things here, so the note may be expanded or modified in the future.

If you have any comments or observations, feel free to let us know.

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