A333830 - OEIS

%I #29 Jul 16 2020 11:47:43

%S 1,2,3,4,5,6,7,8,9,1,9,3,9,18,333,36,29,9,12,2,3,9,135,6,1218,216,9,

%T 126,90,3,9,18,355,15,17,9,21,27,198,4,26,6,75,81,9,64,810,12,18,5,

%U 855,90,297,9,936,5050737477,45,27,20,6,45,99,9,174,446,1000260,4209

%N a(n) is the digit sum of the concatenation of the decimal digits of n,n+1,...,n+k, where k >= 0 and minimal, such that the concatenation is divisible by its digit sum, or -1 if no such sum is known.

%C A heuristic argument, see the companion sequence A333687, suggests that the digit sum should always exist. Also see A333687 for the corresponding values of k for each digit sum and for details of the currently unknown terms.

%C The first escape value is a(76) = -1. - _Georg Fischer_, Jul 16 2020

%H Scott R. Shannon, <a href="/A333830/b333830.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 1 as the digit sum 1 divides 1 itself. Similarly a(2),...,a(9) equal 2,...,9 respectively.

%e a(10) = 1 as the digit sum of 10 is 1 which divides 10.

%e a(11) = 9 as A333687(11) = 2 giving the decimal concatenation 111213 which has a digit sum of 9.

%e a(16) = 36 as A333687(16) = 4 giving the decimal concatenation 1617181920 which has a digit sum of 36.

%Y Cf. A333687, A007953, A332580, A332558, A332563, A332542, A332830, A332867, A005349.

%K sign,base

%O 1,2

%A _Scott R. Shannon_, Apr 07 2020