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A309005 Odd squarefree composite numbers m such that m+2 is prime. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

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

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 *)

PROG

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

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

CROSSREFS

Cf. A024556, A241809, A136354.

Sequence in context: A090999 A123912 A296244 * A225916 A128279 A099611

Adjacent sequences:  A309002 A309003 A309004 * A309006 A309007 A309008

KEYWORD

nonn

AUTHOR

David James Sycamore, Jul 05 2019

STATUS

approved

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)