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 A327810 #41 Jun 14 2020 16:02:29
%S A327810 10,130,651,2997,6643,6886,9222,11950,26691,27741,76449,175850,193662,
%T A327810 626626,704396,723296,749470,755846,883407,1181729,1422773,1798303,
%U A327810 1817179,2347506,2593206,4252232,5415589,10453500,11435450,17099841,17402241,25651017
%N A327810 Numbers that are nontrivially palindromic in two or more consecutive integer bases with non-constant number of digits .
%C A327810 This is a subsequence of A279092. That is, each term of A279092 either has an equal number of digits in all the corresponding consecutive bases, or does not, in which case it belongs to this sequence.
%C A327810 Most numbers in A279092 do not belong to this sequence. That is, "unbalanced" consecutive palindromes are much rarer than "balanced" consecutive palindromes.
%C A327810 Specifically, any subsequence of this sequence that is given by fixing the maximum allowed number of digits in the consecutive bases seems to be finite. In contrast, every such subsequence of A279092 is known to be infinite.
%H A327810 Max Alekseyev, <a href="/A327810/b327810.txt">Table of n, a(n) for n = 1..74</a>
%H A327810 Math StackExchange, <a href="https://math.stackexchange.com/q/3367962/318073">Finitely many palindromes in two consecutive number bases, for fixed and distinct numbers of digits</a>
%e A327810 Number 10 can be written as 2*4^1+2*4^0=(2,2)_{4} in base four as a palindrome, and as 1*3^2+0*3^1+1*3^0=(1,0,1)_{3} in base three as a palindrome. The bases 4,3 are consecutive, and have 2,3 digits in their representations respectively. All of this makes the number 10=a(1) a term of the sequence.
%e A327810 a(1) =10 =(2,2)_{4} =(1,0,1)_{3}
%e A327810 a(2) =130 =(2,0,0,2)_{4} =(1,1,2,1,1)_{3}
%e A327810 a(3) =651 =(3,0,0,3)_{6} =(1,0,1,0,1)_{5}
%e A327810 a(4) =2997 =(5,6,6,5)_{8} =(1,1,5,1,1)_{7}
%e A327810 a(5) =6643 =(1,0,0,0,1,0,0,0,1)_{3} =(1,1,0,0,1,1,1,1,1,0,0,1,1)_{2}
%e A327810 a(6) =6886 =(6,8,8,6)_{10} =(1,0,4,0,1)_{9}
%e A327810 a(7) =9222 =(2,4,3,3,4,2)_{5} =(2,1,0,0,0,1,2)_{4}
%e A327810 a(8) =11950 =(2,3,2,2,2,3,2)_{4} =(1,2,1,1,0,1,1,2,1)_{3}
%e A327810 a(9) =26691 =(3,2,3,3,2,3)_{6} =(1,3,2,3,2,3,1)_{5}
%e A327810 a(10) =27741 =(3,3,2,2,3,3)_{6} =(1,3,4,1,4,3,1)_{5}
%t A327810 c[b1_, d_] := Pick[FromDigits[#, b1 + 1] & /@ #, PalindromeQ[#] && Length[#] > 1 && Length[#] != 2 d + 1 & /@ #] &@IntegerDigits[FromDigits[#, b1] & /@ (Flatten[Outer[List, Range[1, b1 - 1], Sequence @@ ConstantArray[Range[0, b1 - 1], d + 0]], d + 0][[All, Join[Range[d + 1], Reverse[Range[1, d + 0]]]]]), b1 + 1]; a[L_] := DeleteDuplicates[Sort[Select[Join[{10}, Flatten[Table[c[b1, d], {d, 2, Ceiling[Log[2, L]/2] + 1}, {b1, 2, Ceiling[L^(1/(2 d))]}]]], # < L &]]]; a[10^6] (* _Matej Veselovac_, Sep 28 2019 *)
%Y A327810 Cf. A279092, A323742.
%K A327810 nonn,base,hard
%O A327810 1,1
%A A327810 _Matej Veselovac_, Sep 26 2019
%E A327810 Edited and terms a(11) onward added by _Max Alekseyev_, Sep 26 2019
%E A327810 Edited by _Max Alekseyev_, Jun 14 2020