

A115334


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


9



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
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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



