The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A306584

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A306584

For any n >= 0, let f_n be the representation of n in the factorial number system: for any i >= 0, 0 <= f_n(i) <= i and n = Sum_{i >= 0} f_n(i) * i!. The representation of a(n) in the factorial number system, say g, satisfies g(i) = f_n(f_n(i)) for any i >= 0.
(history; published version)

#11 by Sean A. Irvine at Fri Jul 12 17:07:29 EDT 2019

STATUS

proposed

approved

#10 by Rémy Sigrist at Fri Jul 12 17:04:27 EDT 2019

STATUS

editing

proposed

#9 by Rémy Sigrist at Fri Jul 12 14:49:41 EDT 2019

LINKS

Rémy Sigrist, <a href="/A306584/b306584.txt">Table of n, a(n) for n = 0..5040</a>

STATUS

approved

editing

Discussion

Fri Jul 12

17:04

Rémy Sigrist: added b-file

#8 by Susanna Cuyler at Wed Mar 06 08:36:10 EST 2019

STATUS

proposed

approved

#7 by Rémy Sigrist at Sun Mar 03 03:27:52 EST 2019

STATUS

editing

proposed

#6 by Rémy Sigrist at Wed Feb 27 16:07:45 EST 2019

FORMULA

a(n) = A306605(n, n).

CROSSREFS

Cf. A007623, A306605.

#5 by Rémy Sigrist at Tue Feb 26 11:37:24 EST 2019

EXAMPLE

For n = 42:

- 42 = 4! + 3*3!,

- f_42(0) = 0, f_42(f_42(0)) = 0,

- f_42(1) = 0, f_42(f_42(0)) = 0,

- f_42(2) = 0, f_42(f_42(2)) = 0,

- f_42(3) = 3, f_42(f_42(3)) = 3,

- f_42(4) = 1, f_42(f_42(4)) = 0,

- f_42(k) = 0, f_42(f_42(k)) = 0 for any k > 4,

- hence a(42) = 3*3! = 18.

PROG

(PARI) a(n) = { my (f=[]); for (r=1, oo, f = concat(f, n%r); n \= r; if (n==0, return (sum(k=1, #f, f[1+f[k]]*(k-1)!)))) }

#4 by Rémy Sigrist at Tue Feb 26 01:42:51 EST 2019

LINKS

<a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

CROSSREFS

Cf. A007623.

#3 by Rémy Sigrist at Mon Feb 25 14:39:12 EST 2019

NAME

allocated For any n >= 0, let f_n be the representation of n in the factorial number system: for any i >= 0, 0 <= f_n(i) <= i and n = Sum_{i >= 0} f_n(i) * i!. The representation of a(n) in the factorial number system, say g, satisfies g(i) = f_n(f_n(i)) for Rémy Sigristany i >= 0.

DATA

0, 1, 0, 3, 4, 5, 0, 7, 0, 9, 4, 11, 0, 1, 6, 9, 16, 17, 18, 19, 18, 21, 22, 23, 0, 25, 0, 27, 4, 29, 0, 31, 0, 33, 4, 35, 0, 25, 6, 33, 16, 41, 18, 43, 18, 45, 22, 47, 0, 1, 24, 27, 52, 53, 0, 7, 24, 33, 52, 59, 0, 1, 30, 33, 64, 65, 18, 19, 42, 45, 70, 71, 0

OFFSET

0,4

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system">Factorial number system</a>

FORMULA

a(n) <= n.

KEYWORD

allocated

nonn,base

AUTHOR

Rémy Sigrist, Feb 25 2019

STATUS

approved

editing

#2 by Rémy Sigrist at Mon Feb 25 14:39:12 EST 2019

NAME

allocated for Rémy Sigrist

KEYWORD

recycled

allocated