%I #31 Apr 17 2022 12:07:34
%S 1711,1829,2077,2479,3071,3901,5029,6527,6757,7471,7967,8479,10397,
%T 10981,11581,14141,15167,15517,15871,16591,16957,17701,18079,18847,
%U 19631,20837,22927,23791,25567,26941,27877,28829,29797,30287,31279,31781,32287,35941,38117
%N Semiprimes generated by the polynomial 2 * n^2 + 29.
%C 2 * n^2 + 29 is a well-known Legendre prime-producing polynomial which generates 29 distinct primes for n = 0, 1, ..., 28. For n = 29, it yields the first semiprime, 1711 = 29 * 59.
%C The number n = 185 is the least positive integer for which 2*n^2 + 29 = 68479 = 31 * 47 * 47 is not squarefree.
%H K. D. Bajpai, <a href="/A241554/b241554.txt">Table of n, a(n) for n = 1..10000</a>
%H R. A. Mollin, <a href="http://www.jstor.org/stable/2975080">Prime-Producing Quadratics</a>, The American Mathematical Monthly, Vol. 104, No. 6 (Jun. - Jul., 1997), pp. 529-544.
%e 2 * 30^2 + 29 = 1829 = 31 * 59, which is a semiprime and is a term.
%e 2 * 35^2 + 29 = 2479 = 37 * 67, which is a semiprime and is a term.
%p with(numtheory):A241554:= proc() local k; k:=2*x^2+29;if bigomega(k)=2 then RETURN (k); fi; end: seq(A241554(), x=0..500);
%t A241554 = {}; Do[k = 2 * n^2 + 29; If[PrimeOmega[k] == 2, AppendTo[A241554, k]], {n,200}]; A241554
%o (PARI) s=[]; for(n=1, 200, t=2*n^2+29; if(bigomega(t)==2, s=concat(s, t))); s \\ _Colin Barker_, Apr 26 2014
%Y Cf. A007641 (for primes).
%Y Cf. A001358, A072381, A082919, A145292, A228183, A237627, A353004, A353388.
%K nonn
%O 1,1
%A _K. D. Bajpai_, Apr 25 2014