%I #19 Mar 24 2020 06:40:38
%S 2,6,13,57,1614,3686,735417,252641277,4849631998,506364553163
%N Numbers k such that k*prime(k) + 43 is a square.
%e 2 * 3 + 43 = 7^2;
%e 6 * 13 + 43 = 11^2;
%e 13 * 41 + 43 = 24^2;
%e 57 * 269 + 43 = 124^2;
%e 1614 * 13669 + 43 = 4697^2;
%e 3686 * 34501 + 43 = 11277^2;
%e 735417 * 11144513 + 43 = 2862842^2.
%t Select[Range[800000],IntegerQ[Sqrt[# Prime[#]+43]]&] (* _Harvey P. Dale_, Aug 04 2018 *)
%o (Sage)
%o L = primes_first_n(1000000)
%o [n for n in [1..999999] if is_square(n*L[n-1]+43)] # _Tom Edgar_, Jul 10 2014
%Y Cf. A106041, A106042.
%K nonn,more
%O 1,1
%A _Chai Wah Wu_, Jul 09 2014
%E a(8)-a(10) from _Giovanni Resta_, Oct 14 2019