A307730 - OEIS

%I #31 Dec 01 2024 10:03:36

%S 1,2,2,3,3,3,6,4,4,4,4,6,6,6,6,6,9,9,9,9,9,9,9,9,9,12,8,8,8,8,8,8,8,8,

%T 12,12,12,12,12,12,12,12,12,12,12,15,5,5,5,5,5,7,7,7,7,7,7,7,14,10,10,

%U 10,10,10,10,10,10,10,10,14,14,14,14,14,14,14

%N a(n) = A307720(n) * A307720(n+1).

%C For all positive integers n, n appears n times.

%H Rémy Sigrist, <a href="/A307730/b307730.txt">Table of n, a(n) for n = 1..25000</a>

%H Rémy Sigrist, <a href="/A307730/a307730.png">Scatterplot of the first 10000000 terms</a>

%H Rémy Sigrist, <a href="/A307730/a307730.gp.txt">PARI program for A307730</a>

%H N. J. A. Sloane, <a href="/A307730/a307730_1.txt">Table of n, a(n) for n = 1..999999</a>

%e The first terms in this sequence and in A307720 are:

%e   n   a(n)  A307720(n)

%e   --  ----  ----------

%e    1     1           1

%e    2     2           1

%e    3     2           2

%e    4     3           1

%e    5     3           3

%e    6     3           1

%e    7     6           3

%e    8     4           2

%e    9     4           2

%e   10     4           2

%o (PARI) \\ See Links section.

%o (Python)

%o from itertools import islice

%o from collections import Counter

%o def A307730(): # generator of terms. Greedy algorithm

%o     c, b = Counter(), 1

%o     while True:

%o         k, kb = 1, b

%o         while c[kb] >= kb:

%o             k += 1

%o             kb += b

%o         c[kb] += 1

%o         b = k

%o         yield kb

%o A307730_list = list(islice(A307730(),100)) # _Chai Wah Wu_, Oct 21 2021

%Y Cf. A002024, A088178, A307720.

%Y Cf. A348579 (indices of occurrence of each number), A348246 (first occurrence of each number), A348409 (last occurrence).

%K nonn,hear

%O 1,2

%A _Rémy Sigrist_, Apr 25 2019