A289322 -id:A289322 - cp's OEIS frontend

A289323 Number of twos minus number of ones in the first 2^n entries of the Kolakoski sequence, A000002.

-1, 0, 0, 0, 0, -2, 0, 0, -2, 0, -2, 0, -6, 6, 0, 6, 44, 26, -20, -48, 52, 58, 104, -82, -250, -270, -474, -1864, -3094, -4588, -2534, -7574, -1522, 1818, 9264, 18082, 8898, -30500, -20586, -3232, -90522, -127446, -231384, -83574, -87364, 267886

Offset: 0

Richard P. Brent, Jul 05 2017

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This is equivalent to A289322, since a(n) = (#twos)-(#ones) = 2^n-2*(#ones) in the first 2^n entries of A000002.
For example, a(5)=15-17=(32-17)-17=32-2*17=-2 because there are 15 twos and 17 ones in the first 32=2^5 entries of A000002.
The entries in this sequence appear to be of order 2^(n/2), whereas the entries in A289322 are larger (of order 2^n).

			The first 32 entries of the Kolakoski sequence, A000002, are 12211212212211211221211212211211. From this we see that a(5)=15-17=-2, since among the first 2^5 letters, 15 of them are twos and 17 of them are ones.

See references for A289322.

Richard P. Brent, Table of n, a(n) for n = 0..64

Cf. A000002, A054353, A074286, A088568, A156077, A289322.

a(n) = 2^n - 2*A289322(n) = -A088568(2^n) = 2*A054353(2^n) - 3*2^n = 2^n - 2*A156077(2^n).

A289324 Number of twos minus number of ones in the first 10^n entries of the Kolakoski sequence, A000002.

Original entry on oeis.org

-1, 0, 2, -4, 8, 56, 28, -92, -1350, -2446, 4658, -3174, -101402, -16318, -632474, -1954842, 10724544, 45041304, 111069790, 548593100, 1818298480

Offset: 0

Richard P. Brent, Jul 07 2017

This is equivalent to A195206, since a(n) = (#twos)-(#ones) = 10^n-2*(#ones) in the first 10^n entries of A000002.
For example, a(2) = 51 - 49 = (100 - 49) - 49 = 100 - 2*49 = 2 because there are 49 ones and 51 twos in the first 100 = 10^2 entries of A000002.
The entries in this sequence appear to be of order 10^(n/2), whereas the entries in A195206 are larger (of order 10^n).
This sequence is analogous to A289323; the difference is that the indices are powers of ten instead of powers of two.

			The first 10 entries in the Kolakoski sequence, A000002, are 1221121221. There are 5 ones and 5 twos, so a(1) = 5 - 5 = 0.
The first 100=10^2 entries in the Kolakoski sequence A000002 include 49 ones and 51 twos, so a(2) = 51 - 49 = 2.

See the references and links for A195206, A289322.

Cf. A000002, A195206, A054353, A074286, A088568, A156077.

a(n) = 10^n - 2*A195206(n).

Additional (20th) term from Richard P. Brent, Mar 01 2018

cp's OEIS Frontend

A289323 Number of twos minus number of ones in the first 2^n entries of the Kolakoski sequence, A000002.

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