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

1,2

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

P. De Geest, World!Of Numbers

Example

999 = 494 + 505.

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 *)

Crossrefs

Cf. A002113.

Sequence in context: A029950 A372149 A061507 * A061512 A356750 A083964

Adjacent sequences: A046494 A046495 A046496 * A046498 A046499 A046500

Keyword

nonn,base

Author

Patrick De Geest, Sep 15 1998

Extensions

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

Status

approved