A309005 Odd squarefree composite numbers m such that m+2 is prime.

15, 21, 35, 39, 51, 57, 65, 69, 77, 87, 95, 105, 111, 129, 155, 161, 165, 177, 195, 209, 221, 231, 237, 249, 255, 267, 291, 305, 309, 329, 335, 345, 357, 365, 371, 377, 381, 395, 399, 407, 417, 429, 437, 447, 455, 465, 485, 489, 497, 501, 519, 545, 555, 561, 591, 597, 611

Offset: 1

Author

David James Sycamore, Jul 05 2019

Keywords

• nonn

Comments

The squarefree terms of A241809 and A136354 are in this sequence.

Examples

			15 = 3*5 is the smallest squarefree composite number m such that m+2 is prime; 15+2=17.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024556, A241809, A136354.

Programs

Magma

[n: n in [2..611] | IsPrime(n+2) and  not IsPrime(n) and IsSquarefree(n)]; // Vincenzo Librandi, Jul 07 2019

Maple

with(NumberTheory):
N := 500;
for n from 2 to N do
if IsSquareFree(n) and not mod(n, 2) = 0 and not isprime(n) and isprime(n+2) then print(n);
end if:
  end do:

Mathematica

Select[Range[15, 611, 2], And[CompositeQ@ #, SquareFreeQ@ #, PrimeQ[# + 2]] &] (* Michael De Vlieger, Jul 08 2019 *)
Select[Prime[Range[2,150]]-2,SquareFreeQ[#]&&CompositeQ[#]&] (* Harvey P. Dale, Dec 03 2022 *)

PARI

isok(n) = isprime(n+2) && (n%2) && (n>1) && !isprime(n) && issquarefree(n); \\ Michel Marcus, Jul 05 2019