A363764 -id:A363764 - cp's OEIS frontend

A372596 a(1)=-1; thereafter a(n) is (the number of terms that appear with a different frequency from that of a(n-1)) minus (the number of terms that appear with the same frequency).

-1, -1, -2, 1, 0, -1, 0, 3, 2, 1, 2, -1, 4, 7, 6, 5, 4, 1, 12, 7, 4, 9, 10, 9, 8, 11, 10, 7, 10, 5, 14, 17, 16, 15, 14, 15, 12, 9, 8, 11, 8, 5, 0, -5, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 36, 19, 34, 21, 32, 29, 26, 23, 20, 17, 16, 19

Offset: 1

Neal Gersh Tolunsky, May 05 2024

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			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.
The resulting a(n) = t'(n) - t(n) are then:
   n  t'(n)  t(n) a(n)
  --  ----  ----  ----
   1     *     *    -1
   2     0     1    -1
   3     0     2    -2
   4     2     1     1
   5     2     2     0
   6     2     3    -1
   7     3     3     0
   8     5     2     3
   9     5     3     2
  10     5     4     1

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program.
Neal Gersh Tolunsky, Graph of first 200000 terms.

Cf. A372598, A350768, A363764.

PARI
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A372598 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).

Original entry on oeis.org

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

Offset: 1

Neal Gersh Tolunsky, May 06 2024

sign

			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.
  The resulting a(n) = t'(n) - t(n) are then:
   n  t'(n)  t(n) a(n)
  --  ----  ----  ----
   1     *     *    -2
   2     0     1    -1
   3     0     2    -2
   4     1     2    -1
   5     0     4    -4
   6     4     1     3
   7     4     2     2
   8     4     3     1
   9     4     4     0
  10     4     5    -1

Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program.
Neal Gersh Tolunsky, Graph of first 200000 terms.

Cf. A372596, A350768, A363764.

PARI
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\\ See Links section.
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cp's OEIS Frontend

A372596 a(1)=-1; thereafter a(n) is (the number of terms that appear with a different frequency from that of a(n-1)) minus (the number of terms that appear with the same frequency).

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