A178463 The number of iterations for the map : r -> !d(1)+ !d(2)+...+ !d(r) starting with n, needed to reach 0 or stabilize, where d(i), i=1..r, are the decimal digits of n.

2, 1, 2, 3, 10, 33, 6, 7, 31, 9, 2, 1, 2, 3, 10, 33, 6, 7, 31, 9, 3, 2, 3, 4, 3, 25, 25, 6, 32, 26, 4, 3, 4, 11, 2, 23, 6, 27, 31, 14, 3, 10, 3, 2, 32, 24, 22, 25, 40, 16, 25, 33, 25, 23, 24, 8, 28, 44, 32, 34, 25, 6, 25, 6, 22, 28, 27, 27, 17, 13, 6, 7, 6, 27, 25, 44, 27, 33, 21, 16

Offset

0,1

Comments

!k is a subfactorial number (A000166).

a(148349)= 0 because the only number equal to the sum of subfactorials of its digits is :

148349 = !1 + !4 + !8 + !3 + !4 + !9.

Links

Table of n, a(n) for n=0..79.

Example

a(0) = 2 because 0 -> 1->; 0 ;
a(1) = 1 because 1 -> 0 ;
a(2) = 2 because  2 -> 1-> 0 ;
a(3) = 3 because 3 -> 2 -> 1-> 0 ;
a(4) = 10 because 4 -> 9 -> 133496 -> 133774 -> 3721 -> 1857 ->
       16731->2121->2 ->1->0.

Maple

with(numtheory): f:=n->sum(n!*(((-1)^k)*1/k!), k=0..n):for n from 1 to 150 do:it:=1:nn:=n:ind:=0:for  iter from 1 to 50 do: l:=length(nn):n0:=nn:s:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s:=s+f(u): od: nn:=s:if nn<>0 then it:=it+1:else fi:od:printf(`%d,  `, it):od:

Mathematica

g[n_] := Plus @@ Subfactorial /@ IntegerDigits@ n; f[n_] := Length@ Sort@ NestWhileList[ g, n, # != 0 &, 1, 111] - 1; f[0] = 2; Array[f, 80, 0]

Crossrefs

Cf. A000166.

Sequence in context: A337549 A378755 A306456 * A213593 A350026 A118888

Adjacent sequences: A178460 A178461 A178462 * A178464 A178465 A178466

Keyword

nonn,base

Author

Michel Lagneau, Dec 23 2010

Status

approved