A089583 Numbers n which are a multiple of A068505(n) (= n read in base m+1 where m = largest digit of n).

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

Offset: 1

Author

Chuck Seggelin, Nov 08 2003

Keywords

• base
• nonn

Comments

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.

Examples

			a(10)=10 because when 10 is interpreted as base 2 and converted back to base 10, the result, 2, divides evenly into 10.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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).

Programs

Mathematica

bQ[n_]:=Module[{idn=IntegerDigits[n]},Divisible[n,FromDigits[idn, Max[ idn]+1]]]; Select[Range[300],bQ] (* Harvey P. Dale, Aug 30 2014 *)

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

Extensions

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