A082948 Palindromes neither divisible by any of their digits nor by the sum of their digits.

323, 343, 353, 373, 383, 434, 454, 474, 494, 646, 656, 676, 686, 727, 737, 747, 757, 767, 787, 797, 838, 858, 868, 878, 898, 929, 949, 959, 969, 979, 989, 3223, 3443, 3553, 3883, 4334, 4994, 6446, 6886, 7227, 7337, 7447, 7557, 7667, 7887, 7997, 8558, 8668

Offset

1,1

Links

Table of n, a(n) for n=1..48.

Example

868 is a member of the sequence since it is not divisible by 8, 6 or 22. But 4554 is not a member of this sequence. it is not divisible by 4 and 5 but it is divisible by 18.

Maple

digrev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
filter:= proc(n) local L, s;
  L:= convert(n, base, 10);
  s:= convert(L, `+`);
  andmap(t -> n mod t <> 0, {s} union convert(L, set) minus {0})
end proc:
N:=5; # to get all terms of <= N digits
Res:= NULL:
for d from 3 to N do
  if d::even then
    m:= d/2;
    Res:= Res, op(select(filter, [seq(n*10^m + digrev(n), n=3*10^(m-1)..10^m-1)]));
  else
    m:= (d-1)/2;
    Res:= Res, op(select(filter, [seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=[0, $2..9]), n=3*10^(m-1)..10^m-1)]));
  fi
od:
Res; # Robert Israel, Jun 12 2019

Mathematica

ok[n_] := Block[{d = IntegerDigits@ n}, d == Reverse[d] && (d = Select[d, # > 0 &]; Mod[n, Total@ d] > 0 && Min@ Mod[n, d] > 0)]; Select[ Range[ 10^4], ok] (* Giovanni Resta, Jun 12 2019 *)

Crossrefs

Cf. A082947.

Sequence in context: A337781 A340099 A082947 * A182554 A340118 A339517

Adjacent sequences: A082945 A082946 A082947 * A082949 A082950 A082951

Keyword

nonn,base

Author

Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 08 2003

Extensions

Definition edited by Harvey P. Dale, Dec 04 2014

Status

approved