# [seqfan] Re: A tricky sequence [A307720]

Paul Curtz bpcrtz at free.fr
Fri May 3 15:46:58 CEST 2019

```Hello SF,

Via A307707, I also found

a(n) = 0, 1, 2, 4, 6, 10, 13, 18, 22, 29, 34, 42, 48, 58, 65, 76, 84, 97, 106, 120, 130, ... = a(-n-1).

a(4n-1) + a(4n) = 0+0=0, 4+6=10, 18+22=40, 42+48=90, 76+84=160 .... = 10*n^2 = A033583.
Interesting differences. First one: interleave A001651, n+1.

I wish to sumbit a(n).

Best regards,
Paul

----- Mail original -----
De: "Paul Curtz" <bpcrtz at free.fr>
À: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Envoyé: Mercredi 1 Mai 2019 09:50:39
Objet: Re: [seqfan] A tricky sequence [A307720]

Hello SF,
Via A307707, I found
1) 0, 1, 0, 0, 1, 2, 0, 0, 2, 3, 0, 0, 3, 4, 0, 0, ... .
2) 0, 2, 4, 8, 12, 18, 24, 32, 40, ... (A007590=2*A002620)
3) 0, 1, 2, 4,  6, 9,  12, 16, 20, ... (A002620)
4) 0, 1, 2, 4,  5, 8,  10, 14, 16, 21   (first differences: 1, 1, 2, 1, 3, 2, 4, 2, 5, 3, ... = A106466)
5)             2
3   3
5   4   5
6   6   6   6
8   7   8   7   8
9   9   9   9   9   9
...
6) 0, 0, 2, 2, 6, 6, 11, 11, 18, 18, 26, 26, 36, 36, 47, 47, 60, 60, ... .
(0, 2, 6, 11, 18, 26, 36, 47, ... not in OEIS
2, 4,  5, 7,  8, 10, 11, 13, ... = A001651)

Best regards,
Paul

----- Mail original -----
De: "Éric Angelini" <bk263401 at skynet.be>
À: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
Envoyé: Mercredi 24 Avril 2019 11:15:02
Objet: [seqfan] A tricky sequence [A307720]

Hello SeqFans,
a difficult challenge for your computer (and the quantity
of memory it has):

What is the smallest "n" here such that a(n) = 2019?

The sequence exists only so far as a draft in the OEIS:
https://oeis.org/draft/A307720

It says:
Lexicographically earliest sequence starting with a(1) = 1
where a(n) is the number of pairs of contiguous terms whose
product is a(n).

DATA
1, 1, 2, 1, 3, 1, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 4, 2, 4, 2, 4, 2, 4, 2, 4, 3, 4, 3, 4, 3,
4, 3, 4, 3, 4, 3, 5, 1, 5, 1, 5, 1, 7, 1, 7, 1, 7, 1, 7, 2,
5, 2, 5, 2,...

A307720 will show all natural numbers sooner or later -- but,
ahem, more "later" than "sooner"! So, what about 2019?

The "twin" sequence was published yesterday (Belgium's time):
https://oeis.org/A307707

Best,
É.

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```

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