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 A082232 Palindromes divisible by their digit sum. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 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 *) PROG (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 (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 CROSSREFS Sequence in context: A106003 A283868 A087995 * A117228 A032567 A134853 Adjacent sequences: A082229 A082230 A082231 * A082233 A082234 A082235 KEYWORD base,nonn AUTHOR Amarnath Murthy, Apr 09 2003 EXTENSIONS Corrected and extended by Giovanni Resta, Feb 08 2006 More terms from Chai Wah Wu, Aug 22 2014 STATUS approved

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Last modified December 9 11:21 EST 2022. Contains 358700 sequences. (Running on oeis4.)