This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108911 #50 Jun 22 2025 03:09:24
%S A108911 0,0,-3,-20,-115,-714,-5033,-40312,-362871,8,9,9,6,-11,-106,-705,
%T A108911 -5024,-40303,-362862,17,18,18,15,-2,-97,-696,-5015,-40294,-362853,23,
%U A108911 24,24,21,4,-91,-690,-5009,-40288,-362847,15,16,16,13,-4,-99,-698,-5017,-40296,-362855,-71,-70,-70,-73
%N A108911 Difference between n and the sum of the factorials of its digits.
%C A108911 Null values are at n = 1, 2, 145, 40585 (A014080). Twin values are at n = 1, 2; 11, 12; 21, 22; ... 10*i + 1, 10*i + 2. Not in sequence: 7, 10, 14, ... Nice polar diagrams repeating themselves with normalized angle to 9! and radius = a(n).
%C A108911 The sequence can be seen as the difference between the natural numbers in the decimal system (n_dec = N0*(10^0) + N1*(10^1) + N2*(10^2)...) and their values in a non-positional number system based on the factorials of the digits (n_fact = N0*(N0 - 1)! + N1*(N1 - 1)! + N2*(N2 - 1)! ...). See also A111095. Note that a(np) - a(n) is congruent to 0 mod 9 if n and np are different for the permutation of the digits. Example (a(5971) - a(1957))/9 = 446. The property can be easily derived by remembering that np - n is congruent to 0 mod 9. - _Giorgio Balzarotti_, Oct 15 2005
%H A108911 Vincenzo Librandi, <a href="/A108911/b108911.txt">Table of n, a(n) for n = 1..1000</a>
%F A108911 a(n) = n - (N0! + N1! + N2! + ...) if n = N0*10^0 + N1*10^1 + N2*10^2 ...
%F A108911 a(n) = n - A061602(n). - _Michel Marcus_, Apr 21 2014
%e A108911 For n = 35, a(35) = -91 because 35 - (3! + 5!) = 35 - (6 + 120) = -91.
%p A108911 a:= n-> n-add(i!, i=convert(n, base, 10)):
%p A108911 seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 24 2018
%t A108911 f[n_] := n - Plus @@ Factorial /@ IntegerDigits[n]; Table[f[n], {n, 53}] (* _Ray Chandler_, Jul 24 2005 *)
%o A108911 (PARI) a(n) = my(d = digits(n)); n - sum(i=1, #d, d[i]!); \\ _Michel Marcus_, Apr 21 2014
%o A108911 (Magma) [n-&+[Factorial(d): d in Intseq(n)]: n in [1..60]]; // _Bruno Berselli_, Oct 25 2018
%Y A108911 Cf. A005096, A014080, A061602.
%K A108911 sign,base,look,easy
%O A108911 1,3
%A A108911 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jul 18 2005
%E A108911 Extended by _Ray Chandler_, Jul 24 2005