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%I #12 Nov 23 2013 19:47:58
%S 0,1,2,2,3,3,3,3,1,6,3,3,3,2,1,6,2,3,1,3,5,3,1,3,6,2,2,3,10,3,3,3,2,1,
%T 6,2,3,1,3,5,3,1,3,6,2,1,3,5,5,3,10,2,3,1,3,5,3,1,3,6,2,1,2,4,2,4,5,3,
%U 3,9,3,1,3,6,2,1,2,4,2,4,5,3,2,4,3,10
%N After a(0)=0, a(n) = A231713(A219666(n),A219666(n-1)).
%C For all n, a(A226061(n+1)) = A232095(n). This works because at the positions given by each x=A226061(n+1), it holds that A219666(x) = (n+1)!-1, which has a factorial base representation (A007623) of (n,n-1,n-2,...,3,2,1) whose digit sum (A034968) is the n-th triangular number, A000217(n). This in turn is always a new record as at those points, in each significant digit position so far employed, a maximal digit value (for factorial number system) is used, and thus the preceding term, A219666(x-1) cannot have any larger digits in its factorial base representation, and so the differences between their digits (in matching positions) are all nonnegative.
%H Antti Karttunen, <a href="/A231717/b231717.txt">Table of n, a(n) for n = 0..3149</a>
%F a(0)=0, and for n>=1, a(n) = A231713(A219666(n),A219666(n-1)).
%o (Scheme)
%o (define (A231717 n) (if (zero? n) n (A231713bi (A219666 n) (A219666 (- n 1)))))
%Y A231718 gives the positions of ones.
%Y Cf. also A230410, A231719, A232095.
%K nonn
%O 0,3
%A _Antti Karttunen_, Nov 12 2013
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