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Search: id:A089584
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| A089584 |
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Numbers n which are a strict multiple (>1) of A068505(n) (= n read in base m+1 where m = largest digit of n). |
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+0
3
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| 10, 21, 40, 100, 112, 120, 210, 306, 400, 516, 624, 630, 1000, 1010, 1102, 1320, 1344, 1422, 2223, 2240, 2301, 3430, 4000, 10000, 10100, 10101, 10356, 10360, 11220, 12320, 13440, 14220, 20202, 21112, 21210, 21416, 22400, 30303, 33036, 34300
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also: Terms > 9 in A089583 without digit "9". - M. F. Hasler, Apr 05 2009
This sequence excludes the trivial members of A089583. Note that all single digit numbers are excluded 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 once and are therefore excluded. See sequence A089583 for the full sequence including trivial members.
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EXAMPLE
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a(5)=112 because 112 in base 3 yields 14 in base 10, which evenly divides 112 (112/14 = 8). a(21)=2301 because 2301 in base 4 yields 177, which evenly divides 2301 (2301/177=13).
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PROGRAM
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(PARI) is_A089584(n, d, b)={ 10>(b=1+vecmax(d=eval(Vec(Str(n))))) & n%sum(i=1, #d, d[i]*b^(#d-i))==0 }
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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), A089583 (n mod A068505(n) = 0).
Adjacent sequences: A089581 A089582 A089583 this_sequence A089585 A089586 A089587
Sequence in context: A075846 A164714 A060852 this_sequence A095824 A086225 A014007
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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 by M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 05 2009
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