cp's OEIS Frontend

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.

%I A333440 #11 Mar 07 2021 18:00:25
%S A333440 0,11,22,33,44,55,66,77,88,99,1001,1100,1111,1122,1133,1144,1155,1166,
%T A333440 1177,1188,1199,1221,1331,1441,1551,1661,1771,1881,1991,2002,2112,
%U A333440 2200,2211,2222,2233,2244,2255,2266,2277,2288,2299,2332,2442,2552,2662,2772,2882
%N 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.
%C A333440 The term 0 is included by convention (we consider here that it has no digit).
%C A333440 Each term has an even number of digits, and each digit has an even number of occurrences; hence each term belongs to A283871.
%C A333440 This sequence has connections with A014486; in both sequences digits are balanced in some way.
%C A333440 All palindromes with even number of digits belong to this sequence.
%C A333440 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.
%H A333440 Rémy Sigrist, <a href="/A333440/b333440.txt">Table of n, a(n) for n = 1..4159</a> (terms < 10^6)
%F A333440 11 | a(n). - _David A. Corneth_, Mar 07 2021
%e A333440 The digits of 5586557768 can be paired as follows:
%e A333440     (55)(8(6(55)(77)6)8)
%e A333440 so 5586557768 belongs to this sequence.
%o A333440 (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 }
%Y A333440 Cf. A014486, A056524, A283871, A333399.
%K A333440 nonn,base
%O A333440 1,2
%A A333440 _Rémy Sigrist_, Mar 21 2020