Deceptive numbers

Deceptive numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Repunits are numbers that consist entirely of repetitions of the digit one (unity). The notation R_n symbolizes the repunit made up of n ones.

Every prime p larger than 5, evenly divides the the repunit R_p-1.

E.G.

The repunit R₆ is evenly divisible by 7.

111111 / 7 = 15873

The repunit R₄₂ is evenly divisible by 43.

111111111111111111111111111111111111111111 / 43 = 2583979328165374677002583979328165374677

And so on.

There are composite numbers that also have this same property. They are often referred to as deceptive non-primes or deceptive numbers.

The repunit R₉₀ is evenly divisible by the composite number 91.

111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 / 91 = 1221001221001221001221001221001221001221001221001221001221001221001221001221001221001221

Task

• Find and show at least the first 10 deceptive numbers; composite numbers n that evenly divide the repunit R_n-1

See also

• Numbers Aplenty - Deceptive numbers
• OEIS:A000864 - Deceptive nonprimes: composite numbers k that divide the repunit R_{k-1}

Raku

<lang perl6>put (2..∞).hyper.grep( {$_ % 2 && !.is-prime} ).grep( { (1 x ($_ - 1)) %% $_ } )[^25]</lang>

Output:

91 259 451 481 703 1729 2821 2981 3367 4141 4187 5461 6533 6541 6601 7471 7777 8149 8401 8911 10001 11111 12403 13981 14701