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
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