%N a(n) is the maximal difference between successive parts in the minimally runlength-encoded unordered partition of n (A227368(n)).
%C After n=3, only composites may obtain value 0. (But not all of them do; see A227762.) The first nine n for which a(n)=2 are 7, 13, 23, 33, 47, 61, 79, 97, 119, of which all are primes except 33 and 119. Conjecture: these values are given by A227786.
%C Are there any terms larger than 2?
%H Antti Karttunen, <a href="/A227761/b227761.txt">Table of n, a(n) for n = 0..132</a>
%F a(0) = a(1) = 0, and for n>1, a(n) = A043276(A163575(A227368(n))) - 1.
%o (define (A227761 n) (if (< n 2) 0 (- (A043276 (A163575 (A227368 n))) 1)))
%o ;; Alternative version which uses auxiliary functions DIFF and binexp_to_ascpart which can be found in the Program section of A129594:
%o (define (A227761v2 n) (if (< n 2) 0 (apply max (DIFF (binexp_to_ascpart (A227368 n))))))
%Y A227762 gives the positions of zeros, in other words, such n that their minimally runlength-encoded partition consists of identical parts.
%Y Cf. also A227368 (for the concept of minimally runlength-encoded unordered partition).
%A _Antti Karttunen_, Jul 26 2013