A046497 Palindromes expressible as sum of 2 consecutive palindromes.

1, 3, 5, 7, 9, 11, 33, 55, 77, 99, 121, 212, 232, 252, 272, 292, 393, 414, 434, 454, 474, 494, 595, 616, 636, 656, 676, 696, 797, 818, 838, 858, 878, 898, 999, 2112, 2332, 2552, 2772, 2992, 3993, 4114, 4334, 4554, 4774, 4994, 5995, 6116, 6336, 6556, 6776, 6996, 7997, 8118, 8338, 8558

Offset: 1

Author

Patrick De Geest, Sep 15 1998

Keywords

• nonn
• base

Comments

Contains all palindromes such that the middle digit is odd (if number of digits is odd) or middle two digits are odd (if number of digits is even) and all other digits are even; also palindromes where the first and last digits are odd (but not 1) and all other digits are 9. - Robert Israel, Nov 12 2018

Examples

			999 = 494 + 505.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• P. De Geest, World!Of Numbers

Crossrefs

Cf. A002113.

Programs

Maple

ispali:= proc(n) local L;
L:= convert(n, base, 10);
L = ListTools:-Reverse(L)
end proc:
digrev:= proc(n) local L;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
N:=5; Pals:= $0..9:
for d from 2 to N do
  q:= p;
  if d::even then
    m:= d/2;
    Pals:= Pals, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Pals:= Pals, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Pals:= [Pals]:
select(ispali, Pals[1..-2]+Pals[2..-1]); # Robert Israel, Nov 12 2018

Mathematica

palQ[n_] := Reverse[x = IntegerDigits[n]] == x; Select[Total /@ Partition[Select[Range[3500], palQ], 2, 1], palQ] (* Jayanta Basu, Jun 26 2013 *)
nextPalindrome[n_]:=Module[{k=n+1},While[!PalindromeQ[k],k++]; k]; s={}; Do[If[PalindromeQ[n], sum =n +  nextPalindrome[n]; If[PalindromeQ[sum],AppendTo[s, sum]]],{n,0,10000}]; s (* Amiram Eldar, Nov 10 2018 *)
Select[Total/@Partition[Select[Range[0,5000],PalindromeQ],2,1],PalindromeQ] (* Harvey P. Dale, Sep 24 2021 *)

Extensions

a(1)=1 inserted by Alois P. Heinz, Nov 13 2018