cp's OEIS Frontend

A078266 Integer part of the arithmetic mean of all the distinct numbers formed by permuting the digits of concatenation of numbers from 1 to n.

%I A078266 #24 Jan 07 2019 02:15:24
%S A078266 1,16,222,2777,33333,388888,4444444,49999999,555555555,46464646464,
%T A078266 4102564102563,377777777777777,35947712418300653,3508771929824561403,
%U A078266 349206349206349206348,35265700483091787439613,3599999999999999999999999
%N A078266 Integer part of the arithmetic mean of all the distinct numbers formed by permuting the digits of concatenation of numbers from 1 to n.
%C A078266 For n < 10 there are n! distinct numbers.
%H A078266 Chai Wah Wu, <a href="/A078266/b078266.txt">Table of n, a(n) for n = 1..369</a>
%F A078266 a(n) = A007953(A007908(n))*(10^A055642(A007908(n))-1)/(9*A055642(A007908(n))). - _Chai Wah Wu_, Jan 06 2019
%e A078266 a(3) = floor((123 + 132 + 213 + 231 + 312 + 321)/6) = 222;
%e A078266 a(4) = floor((1234 + 1243 + 1324 + 1342 + 1423 + 1432 + ... + 4312 + 4321)/24) = 66660/24 = 2777.
%p A078266 a:= proc(n) local s, t, l;
%p A078266       s:= cat("", seq(i, i=1..n)); t:= length(s);
%p A078266       l:= (p-> seq(coeff(p, x, i), i=0..9))(add(x^parse(s[i]), i=1..t));
%p A078266       floor((10^t-1)/9*add(i*l[i+1], i=1..9)/t)
%p A078266     end:
%p A078266 seq(a(n), n=1..20);  # _Alois P. Heinz_, Jan 05 2019
%o A078266 (PARI) { a(n) = c=vector(10); for(i=1,n, s=eval(Vec(Str(i))); for(j=1,#s,c[s[j]+1]++); ); l=sum(j=1,10,c[j]); (10^l-1)/9*sum(j=1,10,(j-1)*c[j])\l } \\ _Max Alekseyev_
%o A078266 (Python)
%o A078266 def A078266(n):
%o A078266     s = ''.join(str(i) for i in range(1,n+1))
%o A078266     return sum(int(d) for d in s)*(10**len(s)-1)//(9*len(s)) # _Chai Wah Wu_, Jan 04 2019
%Y A078266 Cf. A071268, A078265.
%K A078266 base,nonn
%O A078266 1,2
%A A078266 _Amarnath Murthy_, Nov 24 2002
%E A078266 More terms from _Max Alekseyev_, Jan 24 2012