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

1,2

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).

Links

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A158023 A004271 A004278 * A068670 A371925 A084925

Adjacent sequences: A333180 A333181 A333182 * A333184 A333185 A333186

Keyword

nonn,base,easy

Author

Alexander Goebel, Mar 10 2020

Status

approved