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

1,2

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A190235 A023181 A123065 * A167792 A035547 A018598

Adjacent sequences: A115331 A115332 A115333 * A115335 A115336 A115337

Keyword

nonn

Author

Zak Seidov, Mar 06 2006

Status

approved