A241884 Numbers n such that n - n^2/k^2 is not prime for all k < n.

1, 2, 5, 7, 9, 10, 11, 13, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 39, 40, 41, 43, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 69, 70, 71, 73, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 100

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Apr 30 2014

Keywords

• nonn

Comments

Conjecture: numbers n such that n-1 is not a prime number. - Vincenzo Librandi, Jul 16 2016

Counterexamples to conjecture: 56, 306, 552, 870, ... are not in the sequence. These are p^2+p where p is prime but p^2+p-1 is not prime. - Robert Israel, Jul 04 2017

Examples

			56 is not in the sequence because 56 - 56^2/8^2 = 7 is prime for k = 8.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008864, A036690, A138666 (numbers n such that 2n - n/k is not prime for all k), A242221.

Programs

Maple

filter:= n -> andmap(t -> not isprime(n - t^2), numtheory:-divisors(n)):
select(filter, [$1..1000]); # Robert Israel, Jul 04 2017

PARI

isOK(n) = fordiv(n, k, if(isprime(n-(n/k)^2), return(0))); 1
s=[]; for(n=1, 100, if(isOK(n), s=concat(s, n))); s \\ Colin Barker, May 16 2014