

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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..20.
Hiroaki Yamanouchi, Fast Pythonprogram 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 base2), A261234 (for base3).
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 Pythonprogram by Antti Karttunen, Jun 27 2016


STATUS

approved



