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%I #17 May 14 2024 12:14:04
%S 6,66,88,222,252,272,282,414,444,464,474,606,616,636,666,696,828,858,
%T 868,888,2002,2112,2442,2552,2772,2992,4004,4224,4554,4664,4884,5775,
%U 6006,6336,6666,6776,6996,8008,8118,8228,8448,8778,8888,20202,20502,20802,21012,21112,21312
%N Palindromic Zumkeller numbers in base 10.
%C Intersection of A002113 and A083207.
%C 1x1, where x stands for zero or more zeros, is never divisible by 2 and 3. Since 2*3*1x1 is always a Zumkeller number, it follows that there are infinitely many terms.
%C Based on the conjecture that there are infinitely many repunit primes, one may conjecture there are infinitely many repdigit terms, since 2*3*y (where y is a repunit prime) is a repdigit palindromic Zumkeller number.
%C Note that A098775 is not a subsequence: not every abundant number is a Zumkeller number. E.g., 22122 is in A098775 but is not here. - _Amiram Eldar_, May 05 2024
%H R. J. Mathar, <a href="/A372547/b372547.txt">Table of n, a(n) for n = 1..263</a>
%t zn=Cases[Import["https://oeis.org/A083207/b083207.txt","Table"],{_,_}][[All,2]]; Select[zn,PalindromeQ[#]&]
%Y Cf. A002113, A083207, A098775.
%K nonn,base
%O 1,1
%A _Ivan N. Ianakiev_, May 05 2024
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