This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A029953 #29 Jun 14 2024 11:35:28
%S A029953 0,1,2,3,4,5,7,14,21,28,35,37,43,49,55,61,67,74,80,86,92,98,104,111,
%T A029953 117,123,129,135,141,148,154,160,166,172,178,185,191,197,203,209,215,
%U A029953 217,259,301,343,385,427,434,476,518,560,602,644,651,693,735,777,819
%N A029953 Palindromic in base 6.
%C A029953 Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - _Charles R Greathouse IV_, May 03 2020
%H A029953 T. D. Noe, <a href="/A029953/b029953.txt">Table of n, a(n) for n = 1..10000</a>
%H A029953 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 A029953 Patrick De Geest, <a href="http://www.worldofnumbers.com/nobase10.htm">Palindromic numbers beyond base 10</a>.
%H A029953 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 A029953 <a href="/index/Ab#basis_03">Index entries for sequences that are an additive basis</a>, order 3.
%F A029953 Sum_{n>=2} 1/a(n) = 3.03303318... (Phunphayap and Pongsriiam, 2019). - _Amiram Eldar_, Oct 17 2020
%t A029953 f[n_,b_] := Module[{i=IntegerDigits[n,b]}, i==Reverse[i]]; lst={}; Do[If[f[n,6], AppendTo[lst,n]], {n,1000}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2009 *)
%o A029953 (Magma) [n: n in [0..900] | Intseq(n, 6) eq Reverse(Intseq(n, 6))]; // _Vincenzo Librandi_, Sep 09 2015
%o A029953 (PARI) ispal(n,b=6)=my(d=digits(n,b)); d==Vecrev(d) \\ _Charles R Greathouse IV_, May 03 2020
%o A029953 (Python)
%o A029953 from gmpy2 import digits
%o A029953 from sympy import integer_log
%o A029953 def A029953(n):
%o A029953 if n == 1: return 0
%o A029953 y = 6*(x:=6**integer_log(n>>1,6)[0])
%o A029953 return int((c:=n-x)*x+int(digits(c,6)[-2::-1]or'0',6) if n<x+y else (c:=n-y)*y+int(digits(c,6)[-1::-1]or'0',6)) # _Chai Wah Wu_, Jun 14 2024
%Y A029953 Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.
%K A029953 nonn,base,easy
%O A029953 1,3
%A A029953 _Patrick De Geest_