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A231719 After zero, a(n) = largest m such that m! divides the difference between successive nodes A219666(n-1) and A219666(n) in the infinite trunk of the factorial beanstalk.

%I A231719 #16 Jun 29 2016 00:08:57
%S A231719 0,1,1,1,2,1,2,1,3,2,1,2,1,1,3,2,2,1,3,1,2,1,3,1,1,1,1,2,2,1,2,1,1,3,
%T A231719 2,2,1,3,1,2,1,3,1,1,1,3,1,2,1,2,2,2,1,3,1,2,1,3,1,1,1,3,2,3,2,2,1,2,
%U A231719 1,2,1,3,1,1,1,3,2,3,2,2,1,2,3,2,1,1,1
%N A231719 After zero, a(n) = largest m such that m! divides the difference between successive nodes A219666(n-1) and A219666(n) in the infinite trunk of the factorial beanstalk.
%C A231719 The first 4 occurs at n=2206. The first 5 occurs at n = 361788001015 = A226061(16).
%H A231719 Antti Karttunen, <a href="/A231719/b231719.txt">Table of n, a(n) for n = 0..21622</a>
%F A231719 a(0)=0 and for n>=1, a(n) = A055881(A230406(n)).
%F A231719 For all n, a(A226061(n+1)) = A232096(n).
%t A231719 nn = 1200; m = 1; While[Factorial@ m < nn, m++]; m; t = TakeWhile[
%t A231719 Reverse@ NestList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] &, nn, 182], # <= 1000 &]; {0}~Join~Table[SelectFirst[Reverse@ Range@ 10, Divisible[t[[n]] - t[[n - 1]], #!] &], {n, 2, 87}] (* _Michael De Vlieger_, Jun 27 2016, Version 10.2 *)
%o A231719 (Scheme)
%o A231719 (define (A231719 n) (if (zero? n) n (A055881 (A230406 n))))
%Y A231719 Cf. A055881, A219666, A226061, A230406, A230410, A231717, A232096.
%K A231719 nonn
%O A231719 0,5
%A A231719 _Antti Karttunen_, Nov 12 2013