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.

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

Author

Rémy Sigrist, Mar 21 2020

Keywords

• nonn
• base

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.

Examples

			The digits of 5586557768 can be paired as follows:
    (55)(8(6(55)(77)6)8)
so 5586557768 belongs to this sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..4159 (terms < 10^6)

Crossrefs

Cf. A014486, A056524, A283871, A333399.

Programs

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 }

Formula

11 | a(n). - David A. Corneth, Mar 07 2021