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

Author

Chuck Seggelin, Nov 08 2003

Keywords

• base
• nonn

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.

Examples

			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).
		

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).

Programs

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 }

Extensions

Definition reworded by M. F. Hasler, Apr 05 2009