A283871 -id:A283871 - 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.

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

Rémy Sigrist, Mar 21 2020

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.

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

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

Cf. A014486, A056524, A283871, A333399.

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 }

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

A283870 For all n, the set consisting of the terms {a(1), a(2), a(3), ..., a(n)} has an odd number or 0 of digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 1001, 1010, 1100, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 1212, 1221, 1313, 1331, 1414, 1441, 1515, 1551, 1616, 1661, 1717, 1771, 1818, 1881, 1919, 1991, 2002, 2020, 2112, 2121, 2200, 2211, 2222, 2233, 2244, 2255, 2266, 2277, 2288

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Mar 17 2017

The sequence is started with a(1) = 1 and always extended with the smallest integer not yet present and not leading to a contradiction.

			The set consisting of the first 20 terms is {1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,1001}; we count three 0's, seven 1's, three 2's, three 3's, three 4's, etc. All those quantities of digits are odd numbers.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A283871.

filter:= proc(n) local L; L:= convert(n,base,10);
   andmap(t -> numboccur(t,L)::even, L) end proc:
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, op(select(filter, [$1000..9999])); # Robert Israel, Jan 07 2024

a(n) = A283871(n-10) for n >= 20. - Robert Israel, Jan 07 2024

Definition corrected by Robert Israel, Jan 07 2024

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.

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