A242221 Numbers n such that n - n^2/m^2 and 2n - n/m are not prime for all m.

1, 25, 26, 28, 33, 35, 39, 46, 50, 58, 63, 65, 77, 78, 81, 85, 86, 88, 92, 93, 94, 95, 105, 111, 116, 118, 119, 122, 123, 124, 125, 130, 133, 134, 143, 144, 145, 146, 148, 153, 155, 160, 161, 162, 165, 170, 171, 172, 176, 178, 183, 185, 186, 188, 189, 196, 202

Offset

1,2

Comments

Intersection of A241884 and A138666.

Links

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

Example

26 is in this sequence because:
1) 26 - 26^2/1^2 = -650 and 2*26 - 26/1 = 26 both not prime for m = 1,
2) 26 - 26^2/2^2 = -143 and 2*26 - 26/2 = 39 both not prime for m = 2,
3) 26 - 26^2/13^2 = 22 and 2*26 - 26/13 = 50 both not prime for m = 13,
4) 26 - 26^2/26^2 = 25 and 2*26 - 26/26 = 51 both not prime for m = 26.

Maple

filter:= proc(n) andmap(t -> not isprime(n - n^2/t^2) and not isprime(2*n - n/t), numtheory:-divisors(n)) end proc:
select(filter, [$1..200]); # Robert Israel, Jul 03 2017

Mathematica

filterQ[n_] := AllTrue[Divisors[n], !PrimeQ[n - n^2/#^2] && !PrimeQ[2n - n/#]&];
Select[Range[200], filterQ] (* Jean-François Alcover, Jul 27 2020, after Maple *)

Prog

(PARI) f(n)=fordiv(n, m, if(isprime(n-n^2/m^2), return(0))); 1
g(n)=fordiv(n, m, if(isprime(2*n-n/m), return(0))); 1
for(n=1, 200, if(f(n) && g(n), print1(n, ", "))) \\ Colin Barker, May 08 2014

Crossrefs

Cf. A138666, A241884.

Sequence in context: A046511 A140058 A199992 * A186538 A340271 A003996

Adjacent sequences: A242218 A242219 A242220 * A242222 A242223 A242224

Keyword

nonn

Author

Ilya Lopatin and Juri-Stepan Gerasimov, May 07 2014

Extensions

More terms from Colin Barker, May 08 2014

Example corrected by Colin Barker, May 09 2014

Status

approved