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

1,1

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/

Links

Table of n, a(n) for n=1..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)

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]

Crossrefs

Cf. A000290, A062940, A113119.

Sequence in context: A058722 A318013 A320399 * A227102 A221577 A363383

Adjacent sequences: A173903 A173904 A173905 * A173907 A173908 A173909

Keyword

nonn,base,changed

Author

Robert G. Wilson v, Nov 26 2010

Status

approved