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A302578
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Numbers N such that N modulo N's digitsum is a substring of N.
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1
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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;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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It seems that about third of all numbers belong to the sequence.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[200], SequenceCount[IntegerDigits[#], IntegerDigits[Mod[#, Total[ IntegerDigits[ #]]]]]>0&] (* Harvey P. Dale, Mar 03 2024 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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