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A289324
Number of twos minus number of ones in the first 10^n entries of the Kolakoski sequence, A000002.
0
-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.
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
KEYWORD
sign,more
AUTHOR
Richard P. Brent, Jul 07 2017
EXTENSIONS
Additional (20th) term from Richard P. Brent, Mar 01 2018
STATUS
approved