login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288305 Pairs of a prime number and square of prime number differs by 2. (Pseudo-twin). 1
2, 4, 7, 9, 9, 11, 23, 25, 47, 49, 167, 169, 359, 361, 839, 841, 1367, 1369, 1847, 1849, 2207, 2209, 3719, 3721, 5039, 5041, 7919, 7921, 10607, 10609, 11447, 11449, 16127, 16129, 17159, 17161, 19319, 19321, 29927, 29929, 36479, 36481, 44519, 44521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sum of reciprocals converges and (1/2) + (1/4) + (1/7) + (1/9) + (1/9) + (1/11) + (1/23) +... = 1.3569053... (constant).

Are there infinitely many pairs?

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

MATHEMATICA

Select[Join @@ Map[{{# - 2, #}, {#, # + 2}} &, Prime@ Range[10^4]], MemberQ[Sqrt@ #, _?(And[PrimeQ@ #] &)] &] // Flatten (* Michael De Vlieger, Jun 09 2017 *)

PROG

(PARI) {

forprime(n=2, 300,

              if(isprime(n^2-2), print1(n^2-2, ", "n^2", "));

              if(isprime(n^2+2), print1(n^2, ", "n^2+2", "))

            )

}

(PARI) list(lim)=my(v=List(), t); forprime(p=2, sqrtint(2+lim\1), t=p^2; if(isprime(t-2), listput(v, t-2); listput(v, t)); if(isprime(t+2), listput(v, t); listput(v, t+2))); select(k->k<=lim, Vec(v)) \\ Charles R Greathouse IV, Jun 09 2017

CROSSREFS

Sequence in context: A094446 A071790 A199465 * A081249 A327217 A327207

Adjacent sequences:  A288302 A288303 A288304 * A288306 A288307 A288308

KEYWORD

nonn

AUTHOR

Dimitris Valianatos, Jun 07 2017

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)