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

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

Author

Rémy Sigrist, Jun 24 2022

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Examples

			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.
		

Links

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

Crossrefs

See A355221, A355222 and A355224 for similar sequences.

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

Programs

PARI

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) }

Python

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

Python

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

Formula

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.