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%I #26 Nov 16 2022 15:55:31
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,14,28,42,56,70,84,98,112,126,140,154,
%T 168,170,183,196,209,222,235,248,261,274,287,300,313,326,340,353,366,
%U 379,392,405,418,431,444,457,470,483,496,510,523,536,549,562
%N Numbers that are palindromic in base 13.
%C Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - _Charles R Greathouse IV_, May 04 2020
%H John Cerkan, <a href="/A029958/b029958.txt">Table of n, a(n) for n = 1..10000</a>
%H Javier Cilleruelo, Florian Luca and Lewis Baxter, <a href="https://doi.org/10.1090/mcom/3221">Every positive integer is a sum of three palindromes</a>, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, <a href="http://arxiv.org/abs/1602.06208">arXiv preprint</a>, arXiv:1602.06208 [math.NT], 2017.
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>.
%H Phakhinkon Phunphayap and Prapanpong Pongsriiam, <a href="https://doi.org/10.13140/RG.2.2.23202.79047">Estimates for the Reciprocal Sum of b-adic Palindromes</a>, 2019.
%H <a href="/index/Ab#basis_03">Index entries for sequences that are an additive basis</a>, order 3.
%F Sum_{n>=2} 1/a(n) = 3.55686013... (Phunphayap and Pongsriiam, 2019). - _Amiram Eldar_, Oct 17 2020
%t f[n_,b_]:=Module[{i=IntegerDigits[n,b]},i==Reverse[i]];lst={};Do[If[f[n,13],AppendTo[lst,n]],{n,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2009 *)
%t Select[Range[0,600],IntegerDigits[#,13]==Reverse[IntegerDigits[#,13]]&] (* _Harvey P. Dale_, Nov 16 2022 *)
%o (PARI) isok(n) = my(d=digits(n, 13)); d == Vecrev(d); \\ _Michel Marcus_, May 13 2017
%Y Palindromes in bases 2 through 12: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113, A029956, A029957.
%K nonn,base,easy
%O 1,3
%A _Patrick De Geest_
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