cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A333183 #35 Apr 06 2020 03:52:54
%S A333183 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,
%T A333183 48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,
%U A333183 94,97,100,103,106,109,112,115,118,121,124,127,130,133,136,139,142,145,148,151,154
%N A333183 Number of digits in concatenation of first n positive even integers.
%C A333183 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).
%H A333183 Robert Israel, <a href="/A333183/b333183.txt">Table of n, a(n) for n = 1..10000</a>
%F A333183 a(n) = A058183(n) - Sum_{1..A058183(n)} A000035(A058183(n)).
%F A333183 a(n) = Sum_{i=1..n} (1+floor(log_10(2*i))). - _Robert Israel_, Apr 05 2020
%e A333183 For example, a(5) = 6 because 246810 (the concatenation of the first five positive even integers) has six digits.
%p A333183 L:= [1$4, seq(i $(9/2*10^(i-1),i=2..3)]:
%p A333183 ListTools:-PartialSums(L); # _Robert Israel_, Apr 05 2020
%t A333183 Accumulate[IntegerLength[2Range[80]]] (* _Alonso del Arte_, Mar 12 2020, after _Harvey P. Dale_ *)
%o A333183 (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
%o A333183 (PARI) a(n) = sum(k=1, n, #Str(2*k)); \\ _Michel Marcus_, Apr 02 2020
%Y A333183 Cf. A058183, A007908, A000422, A019520, A038396.
%K A333183 nonn,base,easy
%O A333183 1,2
%A A333183 _Alexander Goebel_, Mar 10 2020