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 A230410 #20 Jun 29 2016 00:21:03
%S A230410 0,1,2,2,2,2,2,2,1,3,2,2,2,2,1,3,1,3,1,3,3,3,1,3,4,2,2,2,4,2,2,2,2,1,
%T A230410 3,1,3,1,3,3,3,1,3,4,2,1,3,3,3,2,4,1,3,1,3,3,3,1,3,4,2,1,2,2,2,2,3,2,
%U A230410 2,4,3,1,3,4,2,1,2,2,2,2,3,2,1,3,2,5,2
%N A230410 After a(0)=0, a(n) = A230415(A219666(n),A219666(n-1)).
%C A230410 After zero, a(n) = number of positions where digits in the factorial base representations of successive nodes A219666(n-1) and A219666(n) in the infinite trunk of the factorial beanstalk differ from each other.
%H A230410 Antti Karttunen, <a href="/A230410/b230410.txt">Table of n, a(n) for n = 0..3149</a>
%F A230410 a(0)=0, and for n>=1, a(n) = A230415(A219666(n),A219666(n-1)).
%F A230410 For all n, a(A226061(n+1)) = A232094(n).
%e A230410 a(8) = 1, because A219666(8)=23, whose factorial base representation (A007623(23)) is '321', and A219666(7)=17, whose factorial base representation (A007623(17)) is '221', and they differ just in one digit position.
%e A230410 a(9) = 3, because A219666(9)=25, '...01001' in factorial base, which differs from '...0321' in three digit positions.
%e A230410 Note that A226061(4)=8 (A226061(n) tells the position of (n!)-1 in A219666), and 1+2+3 = 6 happens to be both a triangular number (A000217) and a factorial number (A000142).
%e A230410 The next time 1 occurs in this sequence because of this coincidence is at x=A226061(16) (whose value is currently not known), as at that point A219666(x) = 16!-1 = 20922789887999, whose factorial base representation is (15,14,13,12,11,10,9,8,7,6,5,4,3,2,1), and A000217(15) = 120 = A000142(5), which means that A219666(x-1) = A219651(20922789887999) = 20922789887879, whose factorial base representation is (15,14,13,12,11,10,9,8,7,6,4,4,3,2,1), which differs only in one position from the previous.
%e A230410 Of course 1's occur in this sequence for other reasons as well.
%t A230410 nn = 1200; m = 1; While[m! < nn, m++]; m; f[n_] := IntegerDigits[n, MixedRadix[Reverse@ Range[2, m]]]; Join[{0}, Function[w, Count[Subtract @@ Map[PadLeft[#, Max@ Map[Length, w]] &, w], k_ /; k != 0]]@ Map[f@ # &, {#1, #2}] & @@@ Partition[#, 2, 1] &@ TakeWhile[Reverse@ NestWhileList[# - Total@ f@ # &, nn, # > 0 &], # <= 500 &]] (* _Michael De Vlieger_, Jun 27 2016, Version 10 *)
%o A230410 (Scheme)
%o A230410 (define (A230410 n) (if (zero? n) n (A230415bi (A219666 n) (A219666 (- n 1))))) ;; Where bi-variate function A230415bi has been given in A230415.
%Y A230410 Cf. A230415, A230406, A231717, A231719, A232094. A230422 gives the positions of ones.
%K A230410 nonn,base
%O A230410 0,3
%A A230410 _Antti Karttunen_, Nov 10 2013