A355221 The k-th leftmost digit of a(n) is the least of the k leftmost digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 20, 21, 22, 22, 22, 22, 22, 22, 22, 22, 30, 31, 32, 33, 33, 33, 33, 33, 33, 33, 40, 41, 42, 43, 44, 44, 44, 44, 44, 44, 50, 51, 52, 53, 54, 55, 55, 55, 55, 55, 60, 61, 62, 63, 64, 65, 66, 66

Offset

0,3

Comments

Leading zeros are ignored.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

a(n) <= n with equality iff n belongs to A009996.

a(a(n)) = a(n).

Example

For n = 1402: min({1}) = 1, min({1, 4}) = 1, min({1, 4, 0}) = 0, min({1, 4, 0, 2}) = 0, so a(1402) = 1100.

Mathematica

Table[FromDigits[Table[Min[Take[IntegerDigits[n], d]], {d, IntegerLength[n]}]], {n, 0, 70}] (* Harvey P. Dale, Jun 30 2023 *)

Prog

(PARI) a(n, base=10) = { my (d=digits(n, base), m=oo); for (k=1, #d, d[k]=m=min(m, d[k])); fromdigits(d, base) }
(Python)
def a(n):
    s, m = str(n), "9"
    return int("".join((m:=min(m, s[k])) for k in range(len(s))))
print([a(n) for n in range(68)]) # Michael S. Branicky, Jun 24 2022
(Python)
from itertools import accumulate
def A355221(n): return int(''.join(accumulate(str(n), func=min))) # Chai Wah Wu, Jun 25 2022

Crossrefs

See A355222, A355223 and A355224 for similar sequences.

Cf. A009996 (fixed points), A342126 (binary analog).

Sequence in context: A121759 A265310 A291576 * A180613 A254948 A072778

Adjacent sequences: A355218 A355219 A355220 * A355222 A355223 A355224

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jun 24 2022

Status

approved