A302578 Numbers N such that N modulo N's digitsum is a substring of N.

10, 11, 13, 14, 17, 19, 20, 22, 23, 26, 28, 30, 31, 32, 33, 35, 37, 39, 40, 41, 44, 46, 50, 53, 55, 60, 62, 64, 66, 69, 70, 71, 73, 77, 80, 82, 88, 90, 91, 93, 96, 99, 100, 101, 102, 103, 104, 106, 108, 109, 110, 113, 118, 119, 120, 121, 122, 123, 125, 127, 129, 131, 136, 139, 140, 142, 145, 149, 150

Offset

1,1

Comments

It seems that about third of all numbers belong to the sequence.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..33333

Example

10 has a digitsum of 1; 10/1 has 0 as remainder; 0 is a substring of 10;
11 has a digitsum of 2; 11/2 has 1 as remainder; 1 is a substring of 11;
12 has a digitsum of 3; 12/3 has 0 as remainder; 0 is not a substring of 12, thus 12 is not in the sequence;
13 has a digitsum of 4; 13/4 has 1 as remainder; 1 is a substring of 13;
...
2018 has a digitsum of 11; 2018 modulo 11 is 5; 5 is not a substring of 2018, thus 2018 is not in the sequence;
etc.

Mathematica

Select[Range[200], SequenceCount[IntegerDigits[#], IntegerDigits[Mod[#, Total[ IntegerDigits[ #]]]]]>0&] (* Harvey P. Dale, Mar 03 2024 *)

Crossrefs

Sequence in context: A107741 A047791 A253610 * A093679 A153194 A175224

Adjacent sequences: A302575 A302576 A302577 * A302579 A302580 A302581

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 10 2018

Status

approved