A115334 Numbers d > 0 such that 3+2d and 3+4d are primes.

1, 2, 4, 5, 7, 10, 14, 17, 19, 20, 25, 32, 34, 40, 47, 49, 52, 55, 62, 67, 77, 82, 89, 94, 95, 104, 110, 115, 119, 124, 130, 140, 154, 157, 164, 172, 185, 209, 214, 215, 220, 227, 229, 242, 259, 272, 280, 287, 292, 305, 307, 314, 319, 320, 322, 325, 329, 349, 362

Offset: 1

Author

Zak Seidov, Mar 06 2006

Keywords

• nonn

Comments

Then { 3, 3+2d, 3+4d } is an arithmetic progression of primes. However, the next term, 3+6d = 3(1+2d), is clearly composite. - Jeppe Stig Nielsen, Jun 20 2022

Examples

			5 is in the sequence because 3 + 2*5 = 13 and 3 + 4*5 = 23 are both prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A160394. [Klaus Brockhaus, May 14 2009]

Programs

Magma

[ n: n in [1..365] | IsPrime(3+2*n) and IsPrime(3+4*n) ]; /* Klaus Brockhaus, May 14 2009 */

Mathematica

Do[If[PrimeQ[{3+2d,3+4d}]=={True,True},Print[d]],{d,100000}]
Select[Range[400],And@@PrimeQ[{3+2#,3+4#}]&] (* Harvey P. Dale, Sep 02 2013 *)

Python

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from (d for d in count(1) if isprime(3+2*d) and isprime(3+4*d))
print(list(islice(agen(), 60))) # Michael S. Branicky, Jun 20 2022

Formula

a(n) = A206037(n)/2. - Wesley Ivan Hurt, Feb 06 2014