A089584 Numbers n which are a proper multiple (>1) of A068505(n) (= n read in base m+1 where m = largest digit of n).

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.

Links

Table of n, a(n) for n=1..40.

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

Adjacent sequences: A089581 A089582 A089583 * A089585 A089586 A089587

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