cp's OEIS Frontend

A333830 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.

%I A333830 #29 Jul 16 2020 11:47:43
%S A333830 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 A333830 126,90,3,9,18,355,15,17,9,21,27,198,4,26,6,75,81,9,64,810,12,18,5,
%U A333830 855,90,297,9,936,5050737477,45,27,20,6,45,99,9,174,446,1000260,4209
%N A333830 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 A333830 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 A333830 The first escape value is a(76) = -1. - _Georg Fischer_, Jul 16 2020
%H A333830 Scott R. Shannon, <a href="/A333830/b333830.txt">Table of n, a(n) for n = 1..1000</a>
%e A333830 a(1) = 1 as the digit sum 1 divides 1 itself. Similarly a(2),...,a(9) equal 2,...,9 respectively.
%e A333830 a(10) = 1 as the digit sum of 10 is 1 which divides 10.
%e A333830 a(11) = 9 as A333687(11) = 2 giving the decimal concatenation 111213 which has a digit sum of 9.
%e A333830 a(16) = 36 as A333687(16) = 4 giving the decimal concatenation 1617181920 which has a digit sum of 36.
%Y A333830 Cf. A333687, A007953, A332580, A332558, A332563, A332542, A332830, A332867, A005349.
%K A333830 sign,base
%O A333830 1,2
%A A333830 _Scott R. Shannon_, Apr 07 2020