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Numbers k such that k*prime(k) + 43 is a square.
0

%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