login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 7 01:51 EST 2022. Contains 358649 sequences. (Running on oeis4.)