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A369347
Numbers whose decimal expansion is quasiperiodic.
0
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jan 21 2024
STATUS
approved