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 A219661 Number of steps to go from (n+1)!-1 to n!-1 with map x -> x - (sum of digits in factorial base representation of x). 14
 1, 2, 5, 19, 83, 428, 2611, 18473, 150726, 1377548, 13851248, 152610108, 1835293041, 23925573979, 335859122743, 5049372125352, 80942722123544, 1378487515335424, 24858383452927384, 473228664468684846 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Hiroaki Yamanouchi, Fast Python-program for computing terms of this sequence FORMULA a(n) = A219652((n+1)!-1) - A219652(n!-1). a(n) = A219662(n) + A219663(n). EXAMPLE (1!)-1 (0) is reached from (2!)-1 (1) with one step by subtracting A034968(1) from 1. (2!)-1 (1) is reached from (3!)-1 (5) with two steps by first subtracting A034968(5) from 5 -> 2, and then subtracting A034968(2) from 2 -> 1. (3!)-1 (5) is reached from (4!)-1 (23) with five steps by repeatedly subtracting the sum of digits in factorial expansion as: 23 - 6 = 17, 17 - 5 = 12, 12 - 2 = 10, 10 - 3 = 7, 7 - 2 = 5. Thus a(1)=1, a(2)=2 and a(3)=5. MATHEMATICA Table[Length@ NestWhileList[# - Total@ IntegerDigits[#, MixedRadix[Reverse@ Range[2, 120]]] &, (n + 1)! - 1, # > n! - 1 &] - 1, {n, 0, 8}] (* Michael De Vlieger, Jun 27 2016, Version 10.2 *) PROG (Scheme) (define (A219661 n) (if (zero? n) n (let loop ((i (-1+ (A000142 (1+ n)))) (steps 1)) (cond ((isA000142? (1+ (A219651 i))) steps) (else (loop (A219651 i) (1+ steps))))))) (define (isA000142? n) (and (> n 0) (let loop ((n n) (i 2)) (cond ((= 1 n) #t) ((not (zero? (modulo n i))) #f) (else (loop (/ n i) (1+ i))))))) ;; Alternative definition: (define (A219661 n) (- (A219652 (-1+ (A000142 (1+ n)))) (A219652 (-1+ (A000142 n))))) CROSSREFS Row sums of A230420 and A230421. Cf. A000142, A007623, A219651, A219652, A219662, A219663, A219665, A226061. Cf. also A213709 (analogous sequence for base-2), A261234 (for base-3). Sequence in context: A138911 A181513 A262165 * A179566 A107377 A286886 Adjacent sequences:  A219658 A219659 A219660 * A219662 A219663 A219664 KEYWORD nonn AUTHOR Antti Karttunen, Dec 03 2012 EXTENSIONS Terms a(16) - a(20) computed with Hiroaki Yamanouchi's Python-program by Antti Karttunen, Jun 27 2016 STATUS approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)