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

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

Offset

0,3

Comments

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.

References

See the references and links for A195206, A289322.

Links

Table of n, a(n) for n=0..20.

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A018422 A058816 A018446 * A338302 A359877 A068620

Adjacent sequences: A289321 A289322 A289323 * A289325 A289326 A289327

Keyword

sign,more

Author

Richard P. Brent, Jul 07 2017

Extensions

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

Status

approved