This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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). 39
 0, 1, 2, 5, 7, 10, 12, 17, 23, 25, 28, 30, 35, 40, 46, 48, 52, 57, 63, 70, 74, 79, 85, 92, 97, 102, 109, 119, 121, 124, 126, 131, 136, 142, 144, 148, 153, 159, 166, 170, 175, 181, 188, 193, 198, 204, 213, 221, 228, 238, 240, 244, 249, 255, 262, 266, 271, 277 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). 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. See A007623 for the factorial number system representation. LINKS Antti Karttunen, Table of n, a(n) for n = 0..21622 FORMULA 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)). a(n) = A230416(A230432(n)). MATHEMATICA 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 *) PROG (Scheme) ;; Memoizing definec-macro from Antti Karttunen's IntSeq-library (definec (A219666 n) (cond ((<= n 2) n) ((= (A226061 (A230411 n)) n) (- (A000142 (A230411 n)) 1)) (else (- (A219666 (+ n 1)) (A034968 (A219666 (+ n 1))))))) ;; Another variant, utilizing A230416 (which gives a more convenient way to compute large number of terms of this sequence): (define (A219666 n) (A230416 (A230432 n))) ;; This function is for checking whether n belongs to this sequence: (define (inA219666? n) (or (zero? n) (= 1 (- (A230418 (+ 1 n)) (A230418 n))))) CROSSREFS Cf. A007623, A034968, A219651, A230411, A226061. For all n, A219652(a(n)) = n and A219653(n) <= a(n) <= A219655(n). Characteristic function: Χ_A219666(n) = A230418(n+1)-A230418(n). The first differences: A230406. Other derived sequences: A230425-A230427, A230430, A230407-A230409, A219662 & A219663, A231723 & A231724, A230420, A230410, A231717, A231719. Subsets: A230428 & A230429. Analogous sequence for binary system: A179016, for Fibonacci number system: A219648. Sequence in context: A206807 A182773 A298869 * A026340 A018717 A188036 Adjacent sequences:  A219663 A219664 A219665 * A219667 A219668 A219669 KEYWORD nonn,base AUTHOR Antti Karttunen, Nov 25 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)