cp's OEIS Frontend

Patterned-digit obtained when (1,5)-half-repdigit is divided by 15, the least such number.This simple generating rule is often[not always] applicable to provide curious digit-patterns. Thus A=1,B=7 give 111..888 numbers divided by 18 results in A003555.

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).

a(1),a(2),a(3),a(4),a(5) are (between the two 0's) the cores of the decimal expansions of a(10),a(11),a(12),a(13),a(14).

First differences begin 130,12300,1223000,122230000,....