Polydivisible number: Difference between revisions

Revision as of 11:15, 3 September 2021

Latest revision as of 19:36, 13 February 2025

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===Estimate for ''F<mathsub>F_bb</sub>''(''n'')</math> and <math>\&Sigma;(''b'')</math>===

[[File:Graph of polydivisible number vectorial.svg|right|thumb|400px|Graph of number of <math>n</math>-digit polydivisible numbers in base 10 <math>F_{10}(n)</math> vs estimate of <math>F_{10}(n)</math>]]

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===Base 10===

The polydivisible numbers in base 10 are

:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 105, 108, 120, 123, 126, 129, 141, 144, 147, 162, 165, 168, 180, 183, 186, 189, 201, 204, 207, 222, 225, 228, 243, 246, 249, 261, 264, 267, 282, 285, 288... {{OEIS|id=A144688}}

The smallest base 10 polydivisible numbers with ''n'' digits are

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==Programming example==

The example below searches for polydivisible numbers in [[Python (programming language)|Python]].

<syntaxhighlight lang="python">

def find_polydivisible(base: int) -> Listlist[int]:

"""Find polydivisible number."""

numbers = []

previous = [i for i in range(1, base)]

for i in range(1, base):

previous.append(i)

new = []

digits = 2

while not previous == []:

numbers.append(previous)

for in in range(0, len(previous)):

for j in range(0, base):

number = previous[i]n * base + j

if number % digits == 0:

new.append(number)

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{{Divisor classes}}

[[Category:Articles with example Python (programming language) code]]

[[Category:Base-dependent integer sequences]]

[[Category:Modular arithmetic]]