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A046497
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Palindromes expressible as sum of 2 consecutive palindromes.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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EXAMPLE
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999 = 494 + 505.
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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