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A288305 Pairs of a prime number and square of prime number differs by 2. (Pseudo-twin). 1

%I

%S 2,4,7,9,9,11,23,25,47,49,167,169,359,361,839,841,1367,1369,1847,1849,

%T 2207,2209,3719,3721,5039,5041,7919,7921,10607,10609,11447,11449,

%U 16127,16129,17159,17161,19319,19321,29927,29929,36479,36481,44519,44521

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

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

%C Are there infinitely many pairs?

%H Charles R Greathouse IV, <a href="/A288305/b288305.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (PARI) {

%o forprime(n=2,300,

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

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

%o )

%o }

%o (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

%K nonn

%O 1,1

%A _Dimitris Valianatos_, Jun 07 2017

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Last modified May 16 18:13 EDT 2021. Contains 343949 sequences. (Running on oeis4.)