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a(n) = log_2( A182105(n) ).
4

%I #30 Sep 27 2019 13:23:36

%S 0,0,1,0,0,1,2,0,0,1,0,0,1,2,3,0,0,1,0,0,1,2,0,0,1,0,0,1,2,3,4,0,0,1,

%T 0,0,1,2,0,0,1,0,0,1,2,3,0,0,1,0,0,1,2,0,0,1,0,0,1,2,3,4,5,0,0,1,0,0,

%U 1,2,0,0,1,0,0,1,2,3,0,0,1,0,0,1,2,0,0,1,0,0,1,2,3,4,0,0,1,0,0,1,2,0,0,1,0,0,1,2,3,0,0,1,0,0,1,2,0,0,1

%N a(n) = log_2( A182105(n) ).

%C Apparently the leftmost positions of change with incrementing skew-binary numbers (A169683), see example. - _Joerg Arndt_, May 27 2016

%C Irregular table read by rows, where the k-th row counts from 0 up to the ruler function of k, A007814(k). - _Allan C. Wechsler_, Sep 26 2019

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Skew_binary_number_system">Skew binary number system</a>

%F a(n) = A082850(n) - 1. - _Omar E. Pol_, Jun 18 2019

%e From _Joerg Arndt_, May 27 2016: (Start)

%e The first nonnegative skew-binary numbers (dots denote zeros) are

%e n : [skew-binary] position of change

%e 00: [ . . . . . ] -

%e 01: [ . . . . 1 ] 0

%e 02: [ . . . . 2 ] 0

%e 03: [ . . . 1 . ] 1

%e 04: [ . . . 1 1 ] 0

%e 05: [ . . . 1 2 ] 0

%e 06: [ . . . 2 . ] 1

%e 07: [ . . 1 . . ] 2

%e 08: [ . . 1 . 1 ] 0

%e 09: [ . . 1 . 2 ] 0

%e 10: [ . . 1 1 . ] 1

%e 11: [ . . 1 1 1 ] 0

%e 12: [ . . 1 1 2 ] 0

%e 13: [ . . 1 2 . ] 1

%e 14: [ . . 2 . . ] 2

%e 15: [ . 1 . . . ] 3

%e 16: [ . 1 . . 1 ] 0

%e 17: [ . 1 . . 2 ] 0

%e 18: [ . 1 . 1 . ] 1

%e 19: [ . 1 . 1 1 ] 0

%e 20: [ . 1 . 1 2 ] 0

%e 21: [ . 1 . 2 . ] 1

%e 22: [ . 1 1 . . ] 2

%e 23: [ . 1 1 . 1 ] 0

%e 24: [ . 1 1 . 2 ] 0

%e 25: [ . 1 1 1 . ] 1

%e 26: [ . 1 1 1 1 ] 0

%e 27: [ . 1 1 1 2 ] 0

%e 28: [ . 1 1 2 . ] 1

%e 29: [ . 1 2 . . ] 2

%e 30: [ . 2 . . . ] 3

%e 31: [ 1 . . . . ] 4

%e 32: [ 1 . . . 1 ] 0

%e 33: [ 1 . . . 2 ] 0

%e ...

%e (End)

%e From _Allan C. Wechsler_, Sep 27 2019 (Start)

%e First few rows of irregular table derived from A007814 (see comments).

%e 0

%e 0 1

%e 0

%e 0 1 2

%e 0

%e 0 1

%e 0

%e 0 1 2 3

%e 0

%e 0 1

%e ...

%e (End)

%Y Cf. A182105, A082850, A007814.

%K nonn

%O 1,7

%A _N. J. A. Sloane_, Aug 01 2012