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%I #30 Oct 17 2020 04:22:00
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,30,45,60,75,90,105,120,135,150,
%T 165,180,195,197,211,225,239,253,267,281,295,309,323,337,351,365,379,
%U 394,408,422,436,450,464,478,492,506,520,534,548,562,576,591
%N Numbers that are palindromic in base 14.
%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="/A029959/b029959.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) = 3.6112482... (Phunphayap and Pongsriiam, 2019). - _Amiram Eldar_, Oct 17 2020
%e 195 is DD in base 14.
%e 196 is 100 in base 14, so it's not in the sequence.
%e 197 is 101 in base 14.
%t palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[ Range[0, 600], palQ[#, 14] &] (* _Harvey P. Dale_, Aug 03 2014 *)
%o (PARI) isok(n) = Pol(d=digits(n, 14)) == Polrev(d); \\ _Michel Marcus_, Mar 12 2017
%Y Palindromes in bases 2 through 13: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113, A029956, A029957, A029958.
%K nonn,base,easy
%O 1,3
%A _Patrick De Geest_
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