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

69, 1410, 21921, 298725, 3792660, 46016727, 541129686, 6221175405, 70311424443, 784112741880, 8651123311875, 94611219470547

Offset: 1

Author

Robert Israel, Mar 05 2020

Keywords

• nonn
• more
• base

Comments

a(n) == 6 (mod 9). - Robert Israel, Mar 06 2020

Examples

			a(1) = 1+4+9+(1+6)+(2+5)+(3+6)+(4+9)+(6+4)+(8+1) = 69.
		

Crossrefs

Cf. A071317.

Programs

Maple

ds:= proc(x) local t,s,r;
  s:= x; t:= 0;
  while s > 0 do
    r:= s mod 10;
    t:= t + r;
    s:= (s-r)/10;
  od;
t
end proc:
seq(add(ds(x^2),x=10^(n-1)..10^n-1), n=1..5);

PARI

for(d=0,6,print1(sum(k=10^d,10^(d+1)-1,vecsum(digits(k^2))),", ")) \\ Hugo Pfoertner, Mar 05 2020

Python

def A333034(n):
    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

Formula

a(n) = A071317(10^n) - A071317(10^(n-1)).

Extensions

a(8)-a(9) from Hugo Pfoertner, Mar 05 2020

a(10)-a(12) from Giovanni Resta, Mar 07 2020