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%I #14 Feb 14 2019 20:22:50
%S 3,11,37,79,137,211,821,991,1597,1831,2081,2347,2927,3571,3917,4657,
%T 5051,6329,8779,9871,11027,14197,14879,17021,20101,21737,26107,27967,
%U 28921,33931,34981,39341,40471,41617,50087,51361,59341,60727,62129,66431,69379,70877
%N Prime numbers in A317298.
%C Conjecture: Except the first term a(1) = 3, all the other terms do not end with 3.
%C It is easy to prove that the numbers A317298(n) end with 3 only when n ends with 1. In this case A317298(10*n+1) = (10*n + 1)*(20*n + 3), which is composite for n > 0. Therefore the conjecture is true. - _Bruno Berselli_, Feb 11 2019
%C Essentially (apart from the 3) the same as A188382, because for even n, A317298(n=2k) has the form 1+2*k+8*k^2 and for odd n A317298(n) is a multiple of n and not prime. - _R. J. Mathar_, Feb 14 2019
%t Select[Table[(1/2)*(1 + (-1)^n + 2*n + 4*n^2),{n,1,300}], PrimeQ]
%o (PARI) for(n=0, 300, if(ispseudoprime(t=(1/2)*(1 + (-1)^n + 2*n + 4*n^2)), print1(t", ")));
%Y Cf. A188382, A317298, A304487.
%K nonn
%O 1,1
%A _Stefano Spezia_, Feb 10 2019
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