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

Author

Rémy Sigrist, Jun 24 2022

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Examples

			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.
		

Links

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

Crossrefs

See A355222, A355223 and A355224 for similar sequences.

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

Programs

Mathematica

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

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

Formula

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

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