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A333440
Numbers where each digit can be paired with a digit of the same value at another position so that two pairs can be nested but cannot otherwise overlap.
3
0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 1001, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 2332, 2442, 2552, 2662, 2772, 2882
OFFSET
1,2
COMMENTS
The term 0 is included by convention (we consider here that it has no digit).
Each term has an even number of digits, and each digit has an even number of occurrences; hence each term belongs to A283871.
This sequence has connections with A014486; in both sequences digits are balanced in some way.
All palindromes with even number of digits belong to this sequence.
For any n > 0, the concatenation of the first n terms of A333399 or the concatenation of the first n+1 terms of A333399 belong to this sequence.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..4159 (terms < 10^6)
FORMULA
11 | a(n). - David A. Corneth, Mar 07 2021
EXAMPLE
The digits of 5586557768 can be paired as follows:
(55)(8(6(55)(77)6)8)
so 5586557768 belongs to this sequence.
PROG
(PARI) is(n, base=10) = { my (u=0, s=0); while (n, my (d=n%base); if (u && s%base==d, u--; s\=base, u++; s=s*base+d); n\=base); u==0 }
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 21 2020
STATUS
approved