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Search: id:A089583
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| A089583 |
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Numbers n which are a multiple of A068505(n) (= n read in base m+1 where m = largest digit of n). |
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+0
2
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 19, 21, 29, 39, 40, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 109, 112, 119, 120, 129, 139, 149, 159, 169, 179, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 209, 210, 219, 229, 239, 249, 259, 269, 279, 289
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Note that all single digit numbers are included as they equal themselves when converted to base b+1. 3 in base 4 is 3 and of course divides evenly into the original value of 3. Note also that all numbers containing the digit 9 can only be interpreted as base 10 numbers, which of course divide themselves. These represent the trivial sequence members. A nontrivial member would be a value like 624, which when interpreted as a base 7 number yields 312 in base 10 which evenly divides 624. See sequence A089584 for the nontrivial members of this sequence.
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EXAMPLE
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a(10)=10 because when 10 is interpreted as base 2 and converted back to base 10, the result, 2, divides evenly into 10.
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PROGRAM
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(PARI) is_A089583(n, d, b)={ 9<(b=1+vecmax(d=eval(Vec(Str(n))))) | n%sum(i=1, #d, d[i]*b^(#d-i))==0 } \\ M. F. Hasler, Apr 05 2009
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CROSSREFS
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Cf. A054055 (largest digit of n), A068505 (n as base b+1 number where b=largest digit of n), A089584 (nontrivial members of this sequence).
Sequence in context: A119246 A108191 A108193 this_sequence A032865 A032889 A009995
Adjacent sequences: A089580 A089581 A089582 this_sequence A089584 A089585 A089586
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KEYWORD
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base,nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 08 2003
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EXTENSIONS
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Definition reworded, minor corrections by M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 05 2009
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