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Conjecture 1. The sequence is unbounded.
Records are 0, 18, 36, 48, ... with indices 1, 13, 19, 43, ... .
The places of nonzero terms correspond to places of those terms of A194658
which are in A164288. Moreover, for n>=1, places of nonzero terms of A194659 and A194186(n+1) coincide. This means that these sequences have the same lengths of the series of zeros.
Conjecture 2. The asymptotic density of nonzero terms is 2/(e^2+1).
Table of n, a(n) for n=1..117.
Cf. A104272, A194658, A194186, A164288
Sequence in context: A195926 A195929 A247604 * A194186 A033668 A030239
Adjacent sequences: A194656 A194657 A194658 * A194660 A194661 A194662
Vladimir Shevelev, Sep 01 2011