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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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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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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LINKS
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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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MATHEMATICA
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bQ[n_]:=Module[{idn=IntegerDigits[n]}, Divisible[n, FromDigits[idn, Max[ idn]+1]]]; Select[Range[300], bQ] (* Harvey P. Dale, Aug 30 2014 *)
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PROG
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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).
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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, Apr 05 2009
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STATUS
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approved
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