A355224 The k-th rightmost digit of a(n) is the greatest of the k rightmost digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 33, 44, 55, 66, 77, 88, 99, 20, 21, 22, 33, 44, 55, 66, 77, 88, 99, 30, 31, 32, 33, 44, 55, 66, 77, 88, 99, 40, 41, 42, 43, 44, 55, 66, 77, 88, 99, 50, 51, 52, 53, 54, 55, 66, 77, 88, 99, 60, 61, 62, 63, 64, 65, 66, 77

Offset: 0

Author

Rémy Sigrist, Jun 24 2022

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Examples

			For n = 1402:
- max({1, 4, 0, 2}) = 4,
- max({4, 0, 2}) = 4,
- max({0, 2}) = 2,
- max({2}) = 2,
- so a(1402) = 4422.
		

Links

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

Crossrefs

See A355221, A355222 and A355223 for similar sequences.

Cf. A009996 (fixed points), A340632 (binary analog).

Programs

Mathematica

Table[FromDigits[Max/@Table[Drop[IntegerDigits[m],n],{n,0,IntegerLength[m]-1}]],{m,0,70}] (* Harvey P. Dale, Nov 17 2024 *)

PARI

a(n, base=10) = { my (d=digits(n, base), m=-oo); forstep (k=#d, 1, -1, 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[-1-k])) for k in range(len(s)))[::-1])
print([a(n) for n in range(68)]) # Michael S. Branicky, Jun 24 2022

Python

from itertools import accumulate
def A355224(n): return int(''.join(accumulate(str(n)[::-1],func=max))[::-1]) # Chai Wah Wu, Jun 25 2022

Formula

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

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