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A213879 Positive palindromes that are not the sum of two positive palindromes.

%I A213879 #37 Feb 16 2025 08:33:17
%S A213879 1,111,131,141,151,161,171,181,191,1331,1441,1551,1661,1771,1881,1991,
%T A213879 10301,10401,10501,10601,10701,10801,10901,11111,11211,11311,11411,
%U A213879 11511,11611,11711,11811,11911,12021,12121,12321,12421,12521,12621,12721,12821
%N A213879 Positive palindromes that are not the sum of two positive palindromes.
%C A213879 These numbers do not occur in A035137.
%H A213879 Alois P. Heinz, <a href="/A213879/b213879.txt">Table of n, a(n) for n = 1..2151</a> (first 111 terms from N. J. A. Sloane)
%H A213879 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H A213879 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%F A213879 ({ A002113 } intersect { A319477 }) minus { 0 }. - _Alois P. Heinz_, Sep 19 2018
%e A213879 22 is not a member because 22 = 11 + 11.
%p A213879 # From _N. J. A. Sloane_, Sep 09 2015: bP is a list of the palindromes
%p A213879 a:={}; M:=400; for n from 3 to M do p:=bP[n];
%p A213879 # is p a sum of two palindromes?
%p A213879 sw:=-1; for i from 2 to n-1 do j:=p-bP[i]; if digrev(j)=j then sw:=1; break; fi;
%p A213879 od;
%p A213879 if sw<0 then a:={op(a),p}; fi; od:
%p A213879 b:=sort(convert(a,list));
%t A213879 lst1 = {}; lst2 = {}; r = 12821; Do[If[FromDigits@Reverse@IntegerDigits[n] == n, AppendTo[lst1, n]], {n, r}]; l = Length[lst1]; Do[s = lst1[[i]] + lst1[[j]]; AppendTo[lst2, s], {i, l - 1}, {j, i}]; Complement[lst1, lst2]
%t A213879 palQ[n_] := Reverse[x = IntegerDigits[n]] == x; t1 = Select[Range[12900], palQ[#] &]; Complement[t1, Union[Flatten[Table[i + j, {i, t1}, {j, t1}]]]] (* _Jayanta Basu_, Jun 15 2013 *)
%Y A213879 Cf. A002113, A014092, A035137, A083142, A088601, A260255, A319477.
%K A213879 base,nonn
%O A213879 1,2
%A A213879 _Arkadiusz Wesolowski_, Jun 23 2012