A372598 - OEIS

%I #30 May 26 2024 08:20:45

%S -2,-1,-2,-1,-4,3,2,1,0,-1,4,-1,4,5,2,3,0,-3,10,9,8,7,6,5,0,19,8,3,16,

%T 11,10,7,4,15,16,7,12,19,10,9,12,9,6,11,8,3,30,37,36,35,34,33,32,31,

%U 30,19,14,33,22,35,20,37,18,39,38,37,18,23,40,39,22,19

%N a(1)=-2; thereafter a(n) is (the number of terms thus far that appear with a different frequency from that of a(n-1)) minus (the number of terms that appear with the same frequency).

%H Neal Gersh Tolunsky, <a href="/A372598/b372598.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A372598/a372598.gp.txt">PARI program</a>.

%H Neal Gersh Tolunsky, <a href="/A372598/a372598_1.png">Graph of first 200000 terms</a>.

%e Let t'(n) be the number of terms that appear with a different frequency from that of a(n-1) and t(n) be the number of remaining terms.

%e   The resulting a(n) = t'(n) - t(n) are then:

%e    n  t'(n)  t(n) a(n)

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

%e    1     *     *    -2

%e    2     0     1    -1

%e    3     0     2    -2

%e    4     1     2    -1

%e    5     0     4    -4

%e    6     4     1     3

%e    7     4     2     2

%e    8     4     3     1

%e    9     4     4     0

%e   10     4     5    -1

%o (PARI) \\ See Links section.

%Y Cf. A372596, A350768, A363764.

%K sign

%O 1,1

%A _Neal Gersh Tolunsky_, May 06 2024