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
Keywords
Examples
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.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *)
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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
Extensions
More terms from Colin Barker, May 08 2014
Example corrected by Colin Barker, May 09 2014
Comments