cp's OEIS Frontend

A333034 a(n) is the sum of the digits of the squares of all n-digit numbers.

%I A333034 #23 Mar 07 2020 07:58:01
%S A333034 69,1410,21921,298725,3792660,46016727,541129686,6221175405,
%T A333034 70311424443,784112741880,8651123311875,94611219470547
%N A333034 a(n) is the sum of the digits of the squares of all n-digit numbers.
%C A333034 a(n) == 6 (mod 9). - _Robert Israel_, Mar 06 2020
%F A333034 a(n) = A071317(10^n) - A071317(10^(n-1)).
%e A333034 a(1) = 1+4+9+(1+6)+(2+5)+(3+6)+(4+9)+(6+4)+(8+1) = 69.
%p A333034 ds:= proc(x) local t,s,r;
%p A333034   s:= x; t:= 0;
%p A333034   while s > 0 do
%p A333034     r:= s mod 10;
%p A333034     t:= t + r;
%p A333034     s:= (s-r)/10;
%p A333034   od;
%p A333034 t
%p A333034 end proc:
%p A333034 seq(add(ds(x^2),x=10^(n-1)..10^n-1), n=1..5);
%o A333034 (PARI) for(d=0,6,print1(sum(k=10^d,10^(d+1)-1,vecsum(digits(k^2))),", ")) \\ _Hugo Pfoertner_, Mar 05 2020
%o A333034 (Python)
%o A333034 def A333034(n):
%o A333034     return sum(int(d) for i in range(10**(n-1),10**n) for d in str(i**2)) # _Chai Wah Wu_, Mar 05 2020
%Y A333034 Cf. A071317.
%K A333034 nonn,more,base
%O A333034 1,1
%A A333034 _Robert Israel_, Mar 05 2020
%E A333034 a(8)-a(9) from _Hugo Pfoertner_, Mar 05 2020
%E A333034 a(10)-a(12) from _Giovanni Resta_, Mar 07 2020