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Numbers y such that sqrt(6*y^2+10)-3 is prime.
2

%I #10 Dec 24 2020 02:40:01

%S 3,13,31,129,29180479,121378881,110778874246369293,263631110418336671,

%T 95129083120198558843838970225921,

%U 213007829848951141529011991896053267187

%N Numbers y such that sqrt(6*y^2+10)-3 is prime.

%C sqrt(p + (p^2-1)/6) for p in A339935.

%C Primes in this sequence include 3, 13, 31. Are there any others?

%H Robert Israel, <a href="/A339945/b339945.txt">Table of n, a(n) for n = 1..15</a>

%e a(3) = 31 is a term because sqrt(6*31^2+10)-3 = 73 is prime.

%p g:= gfun:-rectoproc({a(i+4)-10*a(i+2)+a(i)=0, a(0)=1, a(1)=3, a(2)=13, a(3)= 31},a(i),remember):

%p select(y -> isprime(sqrt(6*y^2+10)-3), map(g, [$1..100]));

%Y Cf. A339935.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Dec 23 2020