1,3

Null values are at n = 1,2,145,40585,... 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)

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 (greenblue(AT)tiscali.it), Oct 15 2005

a(n) = n - (N0! + N1! + N2! + ...) if n = N0*10^0 + N1*10^1 + N2*10^2 ...

Example: n = 35, a(35) = -91 because we have 35 - (3!+ 5!) = 35 - (6 + 120)

a(n) = sum((floor(n/(10^j))-10*floor(n/(10^(j+1))))*10^j-(floor(n/(10^j))-10*floor(n/(1\ 0^(j+1))))!, j=0..floor(log10(n)))

f[n_] := n - Plus @@ Factorial /@ IntegerDigits[n]; Table[f[n], {n, 53}] (*Chandler*)

Cf. A005096.

Sequence in context: A158243 A139471 A154641 this_sequence A005096 A164535 A001652

Adjacent sequences: A108908 A108909 A108910 this_sequence A108912 A108913 A108914

sign,base

Paolo Lava and Giorgio Balzarotti (greenblue(AT)tiscali.it), Jul 18 2005

Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 24 2005