A288305 Pairs of a prime number and square of prime number differs by 2. (Pseudo-twin).

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

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: A071790 A366114 A199465 * A081249 A327217 A327207

Adjacent sequences: A288302 A288303 A288304 * A288306 A288307 A288308

Keyword

nonn

Author

Dimitris Valianatos, Jun 07 2017

Status

approved