A225742 Numbers >= 10 that are divisible by the sum and difference of their digits.

10, 12, 20, 21, 24, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 80, 84, 90, 100, 102, 111, 112, 120, 126, 132, 195, 200, 201, 204, 210, 222, 224, 225, 230, 240, 264, 270, 300, 306, 315, 320, 322, 324, 333, 336, 342, 351, 360, 364, 372, 392, 396, 400

Offset

1,1

Comments

3-digit numbers abc must be divisible by a+b+c and a-b-c.

4-digit numbers abcd must be divisible by a+b+c+d and a-b-c-d, ....

Links

Derek Orr, Table of n, a(n) for n = 1..10000

Example

102 is a term because 102 is divisible by 1+0+2 and it is divisible by 1-0-2.

Maple

filter:= proc(n)
local A, s, d;
A:= convert(n, base, 10);
s:= convert(A, `+`);
d:= 2*A[1]-s;
d <> 0 and n mod s = 0 and n mod d = 0;
end proc:
select(filter, [$10 .. 1000]); # Robert Israel, Aug 12 2014

Prog

(Magma) [n: n in [10..500] | not IsZero(u) and IsDivisibleBy(n, &+t) and IsDivisibleBy(n, u) where u is 2*t[#t]-&+t where t is Intseq(n)]; // Bruno Berselli, Aug 13 2013
(PARI)
for(n=10, 10^3, d=digits(n); if(sumdigits(n)!=2*d[1], if(n%sumdigits(n)==0&&n%(sumdigits(n)-2*d[1])==0, print1(n, ", ")))) \\ Derek Orr, Aug 12 2014

Crossrefs

Sequence in context: A338640 A129845 A075492 * A338855 A221638 A358998

Adjacent sequences: A225739 A225740 A225741 * A225743 A225744 A225745

Keyword

nonn,base,easy

Author

Derek Orr, Aug 04 2013

Status

approved