A355222 The k-th leftmost digit of a(n) is the greatest of the k leftmost digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 22, 22, 23, 24, 25, 26, 27, 28, 29, 33, 33, 33, 33, 34, 35, 36, 37, 38, 39, 44, 44, 44, 44, 44, 45, 46, 47, 48, 49, 55, 55, 55, 55, 55, 55, 56, 57, 58, 59, 66, 66, 66, 66, 66, 66, 66, 67

Offset: 0

Author

Rémy Sigrist, Jun 24 2022

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Examples

			For n = 1402: max({1}) = 1, max({1, 4}) = 4, max({1, 4, 0}) = 4, max({1, 4, 0, 2}) = 4, so a(1402) = 1444.
		

Links

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

Crossrefs

See A355221, A355223 and A355224 for similar sequences.

Cf. A003817 (binary analog), A009994 (fixed points).

Programs

PARI

a(n, base=10) = { my (d=digits(n, base), m=-oo); for (k=1, #d, d[k]=m=max(m, d[k])); fromdigits(d, base) }

Python

def a(n):
    s, m = str(n), "0"
    return int("".join((m:=max(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 A355222(n): return int(''.join(accumulate(str(n),func=max))) # Chai Wah Wu, Jun 25 2022

Formula

a(n) >= n with equality iff n belongs to A009994.

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