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%I #26 Jun 23 2022 15:42:41
%S 0,1,2,3,4,5,6,7,9,18,27,36,45,54,63,65,73,81,89,97,105,113,121,130,
%T 138,146,154,162,170,178,186,195,203,211,219,227,235,243,251,260,268,
%U 276,284,292,300,308,316,325,333,341,349,357,365,373,381,390,398
%N Numbers that are palindromic in base 8.
%C Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - _Charles R Greathouse IV_, May 03 2020
%H T. D. Noe, <a href="/A029803/b029803.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) = 3.2188878... (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,8], AppendTo[lst,n]], {n,1000}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 08 2009 *)
%o (PARI) ispal(n,b=8)=my(d=digits(n,b)); d==Vecrev(d) \\ _Charles R Greathouse IV_, May 03 2020
%o (Python)
%o from itertools import chain, count, islice
%o def A029803_gen(): # generator of terms
%o return chain((0,),chain.from_iterable(chain((int((s:=oct(d)[2:])+s[-2::-1],8) for d in range(8**l,8**(l+1))), (int((s:=oct(d)[2:])+s[::-1],8) for d in range(8**l,8**(l+1)))) for l in count(0)))
%o A029803_list = list(islice(A029803_gen(),20)) # _Chai Wah Wu_, Jun 23 2022
%Y Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.
%K nonn,base,easy
%O 1,3
%A _Patrick De Geest_
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