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

1,2

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.

Links

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

Example

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

Mathematica

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

Prog

(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

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).

Sequence in context: A117241 A108191 A108193 * A264979 A319726 A302589

Adjacent sequences: A089580 A089581 A089582 * A089584 A089585 A089586

Keyword

base,nonn

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Nov 08 2003

Extensions

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

Status

approved