A369347 Numbers whose decimal expansion is quasiperiodic.

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1010, 1111, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2020, 2121, 2222, 2323, 2424, 2525, 2626, 2727, 2828, 2929, 3030, 3131, 3232, 3333, 3434, 3535, 3636, 3737, 3838, 3939

Offset: 1

Author

Rémy Sigrist, Jan 21 2024

Keywords

• nonn
• base

Comments

The decimal representation of a term (ignoring leading zeros) can be covered by (possibly overlapping) occurrences of one of its proper prefixes.

This sequence contains, among others, A020338 and A239019.

The first term that does not belong to A239019 is a(109) = 10101.

Examples

			The number 10101101 belongs to this sequence as its decimal expansion can be covered by copies of its proper prefix 101:
      101
        101
           101
      ........
      10101101
		

Links

• Index entries for sequences related to decimal expansion of n

Crossrefs

Cf. A020338, A239019, A320441 (binary analog).

Programs

PARI

is(w) = { my (tt=0); for (l=1, oo, my (t=w%(10^l)); if (t!=tt, if (t==w, return (0)); my (r=w, g=l); while (g-->=0 && r>=t, r \= 10; if (r%(10^l)==t, if (r==t, return (1), g=l))); tt = t)) }