A343454 - OEIS

%I #8 Apr 15 2021 23:42:06

%S 21,33,35,39,111,339,473,629,735,779,795,801,959,1025,1119,1149,1245,

%T 1253,1281,1575,1589,1695,1851,1919,1961,1985,2199,2315,2523,2561,

%U 2681,2759,3003,3065,3189,3233,3315,3443,3893,3983,4175,4299,4359,4375,4455,4503,4693,4925,5247,5585,5609,5703

%N Numbers k such that k^2+2*A001414(k) and k^2-2*A001414(k) are primes.

%C Square roots of squares in A050705.

%C All terms are odd.

%C Includes 3*p if p, 9*p^2+2*p+6 and 9*p^2-2*p-6 are all primes; the generalized Bunyakovsky conjecture implies there are infinitely many of these.

%H Robert Israel, <a href="/A343454/b343454.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 35 is a term because A001414(35) = 12 and 35^2-2*12 = 1201 and 35^2+2*12 = 1249 are primes.

%p spf:= n -> add(t[1]*t[2],t=ifactors(n)[2]):

%p filter:= proc(n) local s; s:= spf(n); isprime(n^2-2*s) and isprime(n^2+2*s) end proc:

%p select(filter, [seq(i,i=1..10000,2)]);

%Y Cf. A001414, A050705.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Apr 15 2021