A226767 - OEIS

A226767

Let an integer with k+1 digits as n = d(k)*10^k + d(k-1)*10^(k-1) + ... + d(0)*10^0 and consider the transform T(n) = k*10^d(k) + (k-1)*10^d(k-1) + ... + 0*10^d(0). a(n) gives the fixed points of the transform T(n).

%I #15 Jun 18 2013 10:23:19

%S 0,10,120,201,210,1032,1230,2301,2310,3003,3012,3120,3201,3210,10045,

%T 10243,12340,13042,13240,20404,20413,21430,23401,23410,34003,34012,

%U 34120,34201,34210,40006,40015,40123,40204,40213,41032,41230,42301,42310,43003,43012

%N Let an integer with k+1 digits as n = d(k)*10^k + d(k-1)*10^(k-1) + ... + d(0)*10^0 and consider the transform T(n) = k*10^d(k) + (k-1)*10^d(k-1) + ... + 0*10^d(0). a(n) gives the fixed points of the transform T(n).

%C At least one digit of T(n) must be zero otherwise the unitary digit of n is lost.

%H Paolo P. Lava, <a href="/A226767/b226767.txt">Table of n, a(n) for n = 0..1000</a>

%F n = Sum_{j=0..k} j*10^d(j).

%e For n=10045 the transform gives T(10045) = 4*10^1 + 3*10^0+ 2*10^0 + 1*10^4 + 0*10^5 = 40 + 3 + 2 + 10000 + 0 = 10045.

%p with(numtheory); ListA226767:=proc(q) local a,b,k,n;

%p for n from 0 to q do a:=trunc(n/10); b:=0; k:=0;

%p while a>0 do k:=k+1; b:=b+k*10^(a mod 10); a:=trunc(a/10); od;

%p if b=n then print(n); fi; od; end: ListA226767(10^6);

%K nonn,easy,base

%O 0,2

%A _Paolo P. Lava_, Jun 17 2013