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

1, 111, 131, 141, 151, 161, 171, 181, 191, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 10301, 10401, 10501, 10601, 10701, 10801, 10901, 11111, 11211, 11311, 11411, 11511, 11611, 11711, 11811, 11911, 12021, 12121, 12321, 12421, 12521, 12621, 12721, 12821

Offset: 1

Author

Arkadiusz Wesolowski, Jun 23 2012

Keywords

• base
• nonn

Comments

These numbers do not occur in A035137.

Examples

			22 is not a member because 22 = 11 + 11.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2151 (first 111 terms from N. J. A. Sloane)
• Eric Weisstein's World of Mathematics, Palindromic Number
• Index entries for sequences related to palindromes

Crossrefs

Cf. A002113, A014092, A035137, A083142, A088601, A260255, A319477.

Programs

Maple

# From N. J. A. Sloane, Sep 09 2015: bP is a list of the palindromes
a:={}; M:=400; for n from 3 to M do p:=bP[n];
# is p a sum of two palindromes?
sw:=-1; for i from 2 to n-1 do j:=p-bP[i]; if digrev(j)=j then sw:=1; break; fi;
od;
if sw<0 then a:={op(a),p}; fi; od:
b:=sort(convert(a,list));

Mathematica

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]
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 *)

Formula

({ A002113 } intersect { A319477 }) minus { 0 }. - Alois P. Heinz, Sep 19 2018