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A302578 Numbers N such that N modulo N's digitsum is a substring of N. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
It seems that about third of all numbers belong to the sequence.
LINKS
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified March 28 09:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)