cp's OEIS Frontend

A219666 The infinite trunk of factorial expansion beanstalk. The only infinite sequence such that a(n-1) = a(n) - sum of digits in factorial expansion of a(n).

%I A219666 #21 Jun 29 2016 00:20:52
%S A219666 0,1,2,5,7,10,12,17,23,25,28,30,35,40,46,48,52,57,63,70,74,79,85,92,
%T A219666 97,102,109,119,121,124,126,131,136,142,144,148,153,159,166,170,175,
%U A219666 181,188,193,198,204,213,221,228,238,240,244,249,255,262,266,271,277
%N A219666 The infinite trunk of factorial expansion beanstalk. The only infinite sequence such that a(n-1) = a(n) - sum of digits in factorial expansion of a(n).
%C A219666 a(n) tells in what number we end in n steps, when we start climbing up the infinite trunk of the "factorial beanstalk" from its root (zero).
%C A219666 There are many finite sequences such as 0,1,2,4; 0,1,2,5,6; etc. obeying the same condition (see A219659) and as the length increases, so (necessarily) does the similarity to this infinite sequence.
%C A219666 See A007623 for the factorial number system representation.
%H A219666 Antti Karttunen, <a href="/A219666/b219666.txt">Table of n, a(n) for n = 0..21622</a>
%F A219666 a(0) = 0, a(1) = 1, and for n>1, if A226061(A230411(n)) = n then a(n) = A230411(n)!-1, otherwise a(n) = a(n+1) - A034968(a(n+1)).
%F A219666 a(n) = A230416(A230432(n)).
%t A219666 nn = 10^3; m = 1; While[m! < Floor[6 nn/5], m++]; m; t = TakeWhile[Reverse@ NestWhileList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, m]]] &, Floor[6 nn/5], # > 0 &], # <= nn &] (* _Michael De Vlieger_, Jun 27 2016, Version 10.2 *)
%o A219666 (Scheme) ;; Memoizing definec-macro from Antti Karttunen's IntSeq-library
%o A219666 (definec (A219666 n) (cond ((<= n 2) n) ((= (A226061 (A230411 n)) n) (- (A000142 (A230411 n)) 1)) (else (- (A219666 (+ n 1)) (A034968 (A219666 (+ n 1)))))))
%o A219666 ;; Another variant, utilizing A230416 (which gives a more convenient way to compute large number of terms of this sequence):
%o A219666 (define (A219666 n) (A230416 (A230432 n)))
%o A219666 ;; This function is for checking whether n belongs to this sequence:
%o A219666 (define (inA219666? n) (or (zero? n) (= 1 (- (A230418 (+ 1 n)) (A230418 n)))))
%Y A219666 Cf. A007623, A034968, A219651, A230411, A226061. For all n, A219652(a(n)) = n and A219653(n) <= a(n) <= A219655(n).
%Y A219666 Characteristic function: Χ_A219666(n) = A230418(n+1)-A230418(n).
%Y A219666 The first differences: A230406.
%Y A219666 Other derived sequences: A230425-A230427, A230430, A230407-A230409, A219662 & A219663, A231723 & A231724, A230420, A230410, A231717, A231719.
%Y A219666 Subsets: A230428 & A230429.
%Y A219666 Analogous sequence for binary system: A179016, for Fibonacci number system: A219648.
%K A219666 nonn,base
%O A219666 0,3
%A A219666 _Antti Karttunen_, Nov 25 2012