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.

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, 126, 90, 3, 9, 18, 355, 15, 17, 9, 21, 27, 198, 4, 26, 6, 75, 81, 9, 64, 810, 12, 18, 5, 855, 90, 297, 9, 936, 5050737477, 45, 27, 20, 6, 45, 99, 9, 174, 446, 1000260, 4209

Offset

1,2

Comments

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.

The first escape value is a(76) = -1. - Georg Fischer, Jul 16 2020

Links

Scott R. Shannon, Table of n, a(n) for n = 1..1000

Example

a(1) = 1 as the digit sum 1 divides 1 itself. Similarly a(2),...,a(9) equal 2,...,9 respectively.
a(10) = 1 as the digit sum of 10 is 1 which divides 10.
a(11) = 9 as A333687(11) = 2 giving the decimal concatenation 111213 which has a digit sum of 9.
a(16) = 36 as A333687(16) = 4 giving the decimal concatenation 1617181920 which has a digit sum of 36.

Crossrefs

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

Sequence in context: A113009 A068064 A152147 * A067032 A052500 A355632

Adjacent sequences: A333827 A333828 A333829 * A333831 A333832 A333833

Keyword

sign,base

Author

Scott R. Shannon, Apr 07 2020

Status

approved