# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a306584 Showing 1-1 of 1 %I A306584 #11 Jul 12 2019 17:07:29 %S A306584 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, %T A306584 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, %U A306584 0,7,24,33,52,59,0,1,30,33,64,65,18,19,42,45,70,71,0 %N 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. %H A306584 Rémy Sigrist, Table of n, a(n) for n = 0..5040 %H A306584 Wikipedia, Factorial number system %H A306584 Index entries for sequences related to factorial base representation %F A306584 a(n) <= n. %F A306584 a(n) = A306605(n, n). %e A306584 For n = 42: %e A306584 - 42 = 4! + 3*3!, %e A306584 - f_42(0) = 0, f_42(f_42(0)) = 0, %e A306584 - f_42(1) = 0, f_42(f_42(0)) = 0, %e A306584 - f_42(2) = 0, f_42(f_42(2)) = 0, %e A306584 - f_42(3) = 3, f_42(f_42(3)) = 3, %e A306584 - f_42(4) = 1, f_42(f_42(4)) = 0, %e A306584 - f_42(k) = 0, f_42(f_42(k)) = 0 for any k > 4, %e A306584 - hence a(42) = 3*3! = 18. %o A306584 (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)!)))) } %Y A306584 Cf. A007623, A306605. %K A306584 nonn,base %O A306584 0,4 %A A306584 _Rémy Sigrist_, Feb 25 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE