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

1,1

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.

Links

Table of n, a(n) for n=1..48.

Index entries for sequences related to decimal expansion of n

Example

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

Prog

(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)) }

Crossrefs

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

Sequence in context: A299792 A115853 A050785 * A239019 A033023 A014181

Adjacent sequences: A369344 A369345 A369346 * A369348 A369349 A369350

Keyword

nonn,base

Author

Rémy Sigrist, Jan 21 2024

Status

approved