A082232 Palindromes divisible by their digit sum.

1, 2, 3, 4, 5, 6, 7, 8, 9, 111, 171, 222, 252, 333, 414, 444, 555, 666, 777, 828, 888, 999, 2112, 2772, 2992, 4224, 4554, 4774, 6336, 6556, 8118, 8338, 8448, 10101, 10701, 10901, 11511, 12321, 13131, 15751, 18981, 19791, 20202, 20502, 20702, 21012, 21112

Offset: 1

Author

Amarnath Murthy, Apr 09 2003

Keywords

• base
• nonn

References

• P. J. Costello, More Palindromic Niven Numbers, Journal of Recreational Mathematics, vol. 33:1 pp. 18-21 2004-5 Baywood Amityville NY.
• W. McDaniel, Palindromic Niven Numbers, Journal of Recreational Mathematics, vol. 24 pp. 164-6 1992 Baywood Amityville NY.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Programs

Maple

dmax:= 6; # to get all terms with at most dmax digits
f1:= proc(n)
  local L, Ln, i,r,s,p;
  L:= convert(n, base, 10);
  Ln:= nops(L);
r:= add(L[i]*10^(Ln-i), i=1..Ln);
s:= convert(L,`+`);
p:= 10^Ln*n+r;
if p mod (2*s) = 0 then p else NULL fi;
end proc:
f2:= proc(n,d)
local L, Ln, i,r,s,p;
L:= convert(n, base, 10);
Ln:= nops(L);
r:= add(L[i]*10^(Ln-i), i=1..Ln);
s:= convert(L,`+`);
p:= 10^(1+Ln)*n+10^Ln*d+r;
if p mod(2*s+d) = 0 then p else NULL fi;
end proc:
A:= {$1..9}:
for d from 2 to dmax do
  if d::even then
    A:= A union {seq(f1(x),x=10^(d/2-1) .. 10^(d/2)-1)}
  else
    A:= A union {seq(seq(f2(x,y),x=10^((d-1)/2-1) .. 10^((d-1)/2)-1),y=0..9)}
  fi
od:
A; # Robert Israel, Aug 22 2014

Mathematica

d[n_] := IntegerDigits[n]; Select[Range[20800], Reverse[x = d[#]] == x && Divisible[#, Plus @@ d[#]] &] (* Jayanta Basu, Jul 13 2013 *)

PARI

rev(n)=r="";d=digits(n);for(i=1,#d,r=concat(Str(d[i]),r));eval(r)
for(n=1,10^5,if(rev(n)==n,if(n%sumdigits(n)==0,print1(n,", ")))) \\ Derek Orr, Aug 25 2014

Python

A082232 = sorted([int(str(x)+str(x)[::-1]) for x in range(1,10**5) if not
    int(str(x)+str(x)[::-1]) % sum((int(d) for d in str(x)+str(x)[::-1]))]
    + [int(str(x)+str(x)[-2::-1]) for x in range(1,10**5) if not
    int(str(x)+str(x)[-2::-1]) % sum((int(d) for d in str(x)+str(x)[-2::-1]))]) # Chai Wah Wu, Aug 22 2014

Extensions

Corrected and extended by Giovanni Resta, Feb 08 2006

More terms from Chai Wah Wu, Aug 22 2014