A355223 -id:A355223 - cp's OEIS frontend

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

Rémy Sigrist, Jun 24 2022

Leading zeros are ignored.

			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.

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

See A355222, A355223 and A355224 for similar sequences.

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

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

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) }

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

from itertools import accumulate
def A355221(n): return int(''.join(accumulate(str(n),func=min))) # Chai Wah Wu, Jun 25 2022

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

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

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

Original entry on oeis.org

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

Rémy Sigrist, Jun 24 2022

Leading zeros are ignored.

			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.

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

See A355221, A355223 and A355224 for similar sequences.

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

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) }

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

from itertools import accumulate
def A355222(n): return int(''.join(accumulate(str(n),func=max))) # Chai Wah Wu, Jun 25 2022

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

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

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

Original entry on oeis.org

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

Rémy Sigrist, Jun 24 2022

Leading zeros are ignored.

			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.

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

See A355221, A355222 and A355223 for similar sequences.

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

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

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) }

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

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

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

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

cp's OEIS Frontend

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

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

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

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Mathematica

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Python

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