A355222 -id:A355222 - 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).

A355223 The k-th rightmost digit of a(n) is the least of the k rightmost digits of n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0, 11, 22, 23, 24, 25, 26, 27, 28, 29, 0, 11, 22, 33, 34, 35, 36, 37, 38, 39, 0, 11, 22, 33, 44, 45, 46, 47, 48, 49, 0, 11, 22, 33, 44, 55, 56, 57, 58, 59, 0, 11, 22, 33, 44, 55, 66, 67, 68

Offset: 0

Rémy Sigrist, Jun 24 2022

Leading zeros are ignored.

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

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

See A355221, A355222 and A355224 for similar sequences.

Cf. A008592, A009994 (fixed points), A135481 (binary analog).

a(n, base=10) = { my (d=digits(n, base), m=oo); forstep (k=#d, 1, -1, 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[-1-k])) for k in range(len(s)))[::-1])
print([a(n) for n in range(69)]) # Michael S. Branicky, Jun 24 2022

from itertools import accumulate
def A355223(n): return int(''.join(accumulate(str(n)[::-1],func=min))[::-1]) # Chai Wah Wu, Jun 25 2022

a(n) <= n with equality iff n belongs to A009994.
a(a(n)) = a(n).
a(n) = 0 iff n is a multiple of 10.

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Python

Formula

A355223 The k-th rightmost digit of a(n) is the least of the k rightmost digits of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Python

Python

Formula

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Python

Formula