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%I #30 Mar 17 2018 04:03:53
%S 1010,1101,1121,1131,1141,1151,1161,1171,1181,1191,1201,1211,1212,
%T 1231,1241,1251,1261,1271,1281,1291,1301,1311,1313,1321,1341,1351,
%U 1361,1371,1381,1391,1401,1411,1414,1421,1431,1451,1461,1471,1481,1491,1501,1511,1515,1521,1531
%N Pseudo-palindromic numbers: not palindromes (A002113), but a nontrivial palindromic concatenation (AA or ABA) of arbitrary nonzero integers A and B.
%C The pseudo- or almost-palindromic numbers considered here are not related to the similarly named but different concepts mentioned in comments on A003555 and in A060087 - A060088.
%C We could consider "more general" palindromic concatenations like A.B.B.A, A.B.C.B.A, etc., but all of these can be written as A.B'.A with B' = B.B resp. B.C.B, etc. The result is non-palindromic (i.e., not in A002113) as required, if and only if at least one of the strings is non-palindromic.
%C Here, A is allowed to have only one digit, so most of the first 100 terms are of the form 1.B.1 where B = 10, 12, 13, ... (palindromes 11, 22, 33, ... excluded).
%C If all of the strings A, B (...) are required to be non-palindromic, the sequence starts with terms of the form A.A with A = 10, 12, 13, ..., 98: 1010, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2323, .... This is a subsequence of A239019 (numbers which are not primitive words over the alphabet {0,...,9} when written in base 10).
%o (PARI) A286138 = select(t->!is_A002113(t),setunion(vector(801,i,((i-1)\89+1)*1001+((i-1)%89+1)*10),vector(89,i,(i+9)*101))) \\ The first 810 terms.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, May 03 2017