A333183 Number of digits in concatenation of first n positive even integers.

1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154

Offset: 1

Author

Alexander Goebel, Mar 10 2020

Keywords

• nonn
• base
• easy

Comments

Connected with A019520 and A038396, similar to how A058183 applies to both A007908 and A000422 to count the digits in them, as the order of the digits does not matter (2468 returns the same result as 8642).

Examples

			For example, a(5) = 6 because 246810 (the concatenation of the first five positive even integers) has six digits.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A058183, A007908, A000422, A019520, A038396.

Programs

Maple

L:= [1$4, seq(i $(9/2*10^(i-1),i=2..3)]:
ListTools:-PartialSums(L); # Robert Israel, Apr 05 2020

Mathematica

Accumulate[IntegerLength[2Range[80]]] (* Alonso del Arte, Mar 12 2020, after Harvey P. Dale *)

PARI

a(n) = sum(k=1, n, #Str(2*k)); \\ Michel Marcus, Apr 02 2020

Scala

(1 to 80).map{n: Int => new java.math.BigInteger(((2 to (2 * n) by 2).map(.toString)).mkString("")).toString.length} // _Alonso del Arte, Mar 12 2020

Formula

a(n) = A058183(n) - Sum_{1..A058183(n)} A000035(A058183(n)).

a(n) = Sum_{i=1..n} (1+floor(log_10(2*i))). - Robert Israel, Apr 05 2020