A382102 Remove all occurrences of a digit from n such that the resulting number, formed by the remaining digits in their original order, is as small as possible. If no digits remain, a(n)=0.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 0, 3, 3, 3, 3, 3, 3, 0, 1, 2, 3, 0, 4, 4, 4, 4, 4, 0, 1, 2, 3, 4, 0, 5, 5, 5, 5, 0, 1, 2, 3, 4, 5, 0, 6, 6, 6, 0, 1, 2, 3, 4, 5, 6, 0, 7, 7, 0, 1, 2, 3, 4, 5, 6, 7

Offset: 1

Author

Ali Sada, Mar 15 2025

Keywords

• nonn
• base
• look
• nice

Comments

This sequence is inspired by a joke from Finnish comedian ISMO: "The hardest part in English for me is silent letters. You write them down but never say. But since you have silent letters in the language, why don’t you also have silent numbers? They would be far more useful. Like, I owe you 75 dollars, but the 7 is silent.

Starts to differ from A382056 at n=102. - R. J. Mathar, Mar 23 2025

Examples

			For n = 95, we remove (all copies of) the digit 9 and we get a(n) = 5.
For n = 88, we remove all copies of the digit 8 and we get a(88) = 0.
For n = 1917, we remove all copies of the digit 1 and we get a(n) = 97.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A382056.

Programs

Mathematica

A382102[n_] := Min[Table[FromDigits[DeleteCases[#, d]], {d, DeleteDuplicates[#]}] & [IntegerDigits[n]]];
Array[A382102, 100] (* Paolo Xausa, Mar 23 2025 *)

PARI

a(n, base = 10) = { my (d = digits(n, base), s = Set(d)); vecmin(apply(r -> fromdigits(select(t -> t!=r, d), base), s)) } \\ Rémy Sigrist, Mar 23 2025

Python

def f(s, r):
    return int(s) if (s:=s.replace(r, "")) != "" else 0
def a(n):
    s = str(n)
    return min(f(s, d) for d in set(s))
print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Mar 16 2025