A173906 Total number of digits of the squares of all n-digit numbers.

16, 338, 5183, 69837, 878377, 10583772, 123837722, 1418377223, 15983772233, 177837722339, 1958377223398, 21383772233983, 231837722339831, 2498377223398316, 26783772233983162, 285837722339831620, 3038377223398316206, 32183772233983162066, 339837722339831620668, 3578377223398316206680

Offset: 1

Author

Robert G. Wilson v, Nov 26 2010

Keywords

• nonn
• base

Comments

Sequence inspired by Claudio Meller's email to [seqfan] 07:01 a.m., Nov 26 2010, subject: About a problem of Bernardo Recamán Santos found in http://www.mathpuzzle.com/

Crossrefs

Cf. A000290, A062940, A113119.

Programs

Mathematica

f[n_] := Block[{br = 1+ Floor[10^(n-1)*Sqrt@10]},(2n-1)(br-10^(n-1)) + 2n(10^n-br)]; Array[f, 20]

Formula

Limit_{n->oo} a(n)/(n*10^n) = 9/5. [corrected by Jason Yuen, Feb 07 2025]

From Jason Yuen, Feb 07 2025: (Start)

a(n) = (2*n-1)*A062940(2*n-1) + (2*n)*A062940(2*n).

a(n) = (9/5)*n*10^n - ceiling((sqrt(10)-1)*10^(n-1)) for n > 1. (End)