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Number of twos minus number of ones in the first 10^n entries of the Kolakoski sequence, A000002.
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%I #12 Mar 01 2018 07:41:12

%S -1,0,2,-4,8,56,28,-92,-1350,-2446,4658,-3174,-101402,-16318,-632474,

%T -1954842,10724544,45041304,111069790,548593100,1818298480

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

%C This is equivalent to A195206, since a(n) = (#twos)-(#ones) = 10^n-2*(#ones) in the first 10^n entries of A000002.

%C 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.

%C The entries in this sequence appear to be of order 10^(n/2), whereas the entries in A195206 are larger (of order 10^n).

%C This sequence is analogous to A289323; the difference is that the indices are powers of ten instead of powers of two.

%D See the references and links for A195206, A289322.

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

%e The first 10 entries in the Kolakoski sequence, A000002, are 1221121221. There are 5 ones and 5 twos, so a(1) = 5 - 5 = 0.

%e The first 100=10^2 entries in the Kolakoski sequence A000002 include 49 ones and 51 twos, so a(2) = 51 - 49 = 2.

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

%K sign,more

%O 0,3

%A _Richard P. Brent_, Jul 07 2017

%E Additional (20th) term from _Richard P. Brent_, Mar 01 2018