A130761 - OEIS

%I #10 Jun 28 2020 19:21:20

%S 3,5,7,11,13,19,29,31,37,41,43,53,59,61,67,71,79,83,97,107,127,139,

%T 149,157,179,181,191,197,227,229,239,251,263,283,293,307,347,349,353,

%U 373,419,439,443,463,467,479,499,523,541,569,601,607,613,617,619

%N Primes prime(n) such that at least one of the two numbers (prime(n+2)^2-prime(n)^2)/2 - 1 and (prime(n+2)^2-prime(n)^2)/2 + 1 is prime.

%H Robert Israel, <a href="/A130761/b130761.txt">Table of n, a(n) for n = 1..10000</a>

%e (7^2 - 3^2)/2 - 1 is 19. Therefore 3 is in the sequence.

%e (19^2 - 13^2)/2 + 1 is 97. Hence 13 is in the sequence.

%p Res:= NULL:

%p p:= 5: q:= 3:

%p count:= 0:

%p while count < 100 do

%p   r:= q; q:= p; p:= nextprime(p);

%p   v:= (p^2-r^2)/2;

%p   if isprime(v+1) or isprime(v-1) then

%p     count:= count+1; Res:= Res, r;

%p   fi

%p od:

%p Res; # _Robert Israel_, Oct 03 2018

%t Prime[Select[Range[140], PrimeQ[(Prime[ #+2]^2-Prime[ # ]^2)/2+1] || PrimeQ[(Prime[ # +2]^2-Prime[ # ]^2)/2-1] &]]

%t Select[Partition[Prime[Range[200]],3,1],AnyTrue[(#[[3]]^2-#[[1]]^2)/2+{1,-1},PrimeQ]&][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 28 2020 *)

%K nonn,less

%O 1,1

%A _J. M. Bergot_, Jul 13 2007

%E Edited and extended by _Stefan Steinerberger_, Jul 23 2007