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 A226536 #9 Feb 16 2025 08:33:20
%S A226536 828,18281,818,28182,8281828,828,353,747,66,2662,77,757,99,999,99,959,
%T A226536 595,66,9669,696,676,77,2772,66,303,353,535,525,66,66,919,39193,0,30,
%U A226536 99,181,66,0,33,595,323,232,434,94349,323,33,88,525,101,11,383,70,99,88,4884,44,606,66,808,22
%N A226536 Palindromes of length greater than 1 in decimal expansion of e (A001113).
%C A226536 Begin with the left (most significant) k digits and sequentially remove the first j leading digits until a palindrome is found; continue.
%C A226536 a(33) is actually '00', a(34) is actually '030' (which should be obvious), a(38) is actually '00'.
%C A226536 If e is normal number then all multidigit palindromes should appear.
%H A226536 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/NormalNumber.html">Normal Number</a>
%H A226536 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e A226536 e = 2.7182818284590452353602874713526624977572470936999595749669676...
%e A226536 a(1) = 828, as the first nontrivial palindrome in E is '828', which appears in the digits 4 through 6.
%e A226536 a(2) = 18281, as the second nontrivial palindrome in E is '18281', which appears in the digits 3 through 7.
%e A226536 Please note that a(1) runs from digits 4-6 whereas a(2) runs from 3-7. This is why a(1) appears before a(2).
%t A226536 e = RealDigits[E, 10, 250][[1]]; palQ[n_] := n == Reverse[n]; k = 2; lst = {}; While[k < 251, While[j < k, If[ palQ[ Take[e, {j, k}]], p = FromDigits[Take[e, {j, k}]]; AppendTo[lst, p]; Print[p]]; j++]; k++; j = 1]
%Y A226536 Cf. A001113, A002113, A068046, A099052.
%K A226536 nonn,base
%O A226536 1,1
%A A226536 _Reinhard Zumkeller_ and _Robert G. Wilson v_, Jun 09 2013