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

1,2

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

Cf. A014486, A056524, A283871, A333399.

Sequence in context: A283871 A240927 A272655 * A056524 A110745 A280826

Adjacent sequences: A333437 A333438 A333439 * A333441 A333442 A333443

Keyword

nonn,base

Author

Rémy Sigrist, Mar 21 2020

Status

approved