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

0,3

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

Mathematica

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

Prog

(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

Crossrefs

See A355221, A355222 and A355223 for similar sequences.

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

Sequence in context: A276512 A023792 A221221 * A178354 A179309 A032946

Adjacent sequences: A355221 A355222 A355223 * A355225 A355226 A355227

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jun 24 2022

Status

approved