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A089584
Numbers n which are a proper multiple (>1) of A068505(n) (= n read in base m+1 where m = largest digit of n).
2
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
OFFSET
1,1
COMMENTS
Terms > 9 in A089583 without digit "9". - M. F. Hasler, Apr 05 2009
This sequence excludes the trivial terms 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 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 terms.
EXAMPLE
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).
PROG
(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 }
CROSSREFS
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).
Sequence in context: A345962 A195142 A256884 * A192743 A280435 A095824
KEYWORD
base,nonn
AUTHOR
Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 08 2003
EXTENSIONS
Definition reworded by M. F. Hasler, Apr 05 2009
STATUS
approved