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A286138 Pseudo-palindromic numbers: not palindromes (A002113), but a nontrivial palindromic concatenation (AA or ABA) of arbitrary nonzero integers A and B. 1
1010, 1101, 1121, 1131, 1141, 1151, 1161, 1171, 1181, 1191, 1201, 1211, 1212, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1301, 1311, 1313, 1321, 1341, 1351, 1361, 1371, 1381, 1391, 1401, 1411, 1414, 1421, 1431, 1451, 1461, 1471, 1481, 1491, 1501, 1511, 1515, 1521, 1531 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

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.

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).

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).

LINKS

Table of n, a(n) for n=1..45.

PROG

(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.

CROSSREFS

Sequence in context: A082461 A071998 A043640 * A145808 A252683 A157010

Adjacent sequences:  A286135 A286136 A286137 * A286139 A286140 A286141

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, May 03 2017

STATUS

approved

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Last modified February 19 00:35 EST 2020. Contains 332028 sequences. (Running on oeis4.)