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Omni-MATH / Call a number feared if it contains the digits 13 as a contiguous substring and…

Problem

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problem

Call a number feared if it contains the digits 13 as a contiguous substring and fearless otherwise. (For example, 132 is feared, while 123 is fearless.) Compute the smallest positive integer nn such that there exists a positive integer a<100a<100 such that nn and n+10an+10 a are fearless while n+a,n+2a,…,n+9an+a, n+2 a, \ldots, n+9 a are all feared.
Plain-text mathematical notation (without MathML)
Call a number feared if it contains the digits 13 as a contiguous substring and fearless otherwise. (For example, 132 is feared, while 123 is fearless.) Compute the smallest positive integer n such that there exists a positive integer a<100 such that n and n+10a are fearless while n+a,n+2a,…,n+9a are all feared.
Original LaTeX notation
Call a number feared if it contains the digits 13 as a contiguous substring and fearless otherwise. (For example, 132 is feared, while 123 is fearless.) Compute the smallest positive integer $n$ such that there exists a positive integer $a<100$ such that $n$ and $n+10 a$ are fearless while $n+a, n+2 a, \ldots, n+9 a$ are all feared.

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Source and history

task_id
6fed6697-a6ce-5faf-93c8-d4a7e2806a00
task_key
test--6fed6697-a6ce-5faf-93c8-d4a7e2806a00
task_revision_id
1
config / split
/ test

Official source

initial import