This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227761 #23 Jul 20 2019 00:59:10 %S A227761 0,0,0,0,0,1,0,2,0,0,0,1,0,2,1,0,0,1,1,1,0,1,1,2,0,0,1,1,0,1,0,1,1,2, %T A227761 1,0,0,1,1,1,1,1,0,1,1,1,1,2,0,0,1,1,1,1,0,1,0,1,1,1,1,2,1,0,0,1,1,1, %U A227761 1,1,1,1,0,1,1,1,1,1,1,2,0,0,1,1,1,1,1 %N A227761 a(n) is the maximal difference between successive parts in the minimally runlength-encoded unordered partition of n (A227368(n)). %C A227761 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 A227761 Are there any terms larger than 2? %H A227761 Antti Karttunen, <a href="/A227761/b227761.txt">Table of n, a(n) for n = 0..132</a> %F A227761 a(0) = a(1) = 0, and for n>1, a(n) = A043276(A163575(A227368(n))) - 1. %o A227761 (Scheme) %o A227761 (define (A227761 n) (if (< n 2) 0 (- (A043276 (A163575 (A227368 n))) 1))) %o A227761 ;; Alternative version which uses auxiliary functions DIFF and binexp_to_ascpart which can be found in the Program section of A129594: %o A227761 (define (A227761v2 n) (if (< n 2) 0 (apply max (DIFF (binexp_to_ascpart (A227368 n)))))) %Y A227761 A227762 gives the positions of zeros, in other words, such n that their minimally runlength-encoded partition consists of identical parts. %Y A227761 Cf. also A227368 (for the concept of minimally runlength-encoded unordered partition). %K A227761 nonn %O A227761 0,8 %A A227761 _Antti Karttunen_, Jul 26 2013