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%I #17 Feb 23 2016 13:19:19
%S 1,1,2,3,2,1,4,2,1,6,7,1,10,19,25
%N Real part of Gaussian prime numbers such that the Gaussian Primorial product up to them is a Gaussian prime minus one.
%C Consider the Gaussian primes of the first quadrant a+bi, with a>0, b>=0, ordered as a sequence by the size of the norm and the size of the real part a, as defined in A103431. The product of these primes up to a+bi, written here as cp#, may have the property that cp#+1 is a Gaussian prime. a(n) is the real part a of such a+bi. cp#+1 is not necessarily in the first quadrant.
%C Consider the partial products of the complex sequence A103431(n)+A103432(n)*i, which starts p# = 1+i, -1+3i, -5+5i, -15+15i, -75-15i, -195-195i, 585-975i, 3315-3315i,.. If 1+p# is a Gaussian prime, we insert the real part of the last factor, A103431(n), into this sequence. The first missing element is A103431(6), meaning -194-195i is not a Gaussian prime. - _R. J. Mathar_, Jun 13 2011
%C The 7 is for products up to norm 192, the 1 for products up to 256, the 10 for 268, 19 up to 360 and the 25 up to 820. (No further up to norm 5700. Is the sequence finite?) - _R. J. Mathar_, Jun 13 2011
%H Sven Simon, <a href="/A106377/a106377_1.txt">List for A106377/A106378</a>
%e (1+i)*(1+2i)*(2+i)*3*(2+3i) + 1 = (-75-15i) + 1 = (-74-15i), which is a Gaussian prime. This is the 5th number with the property, so a(5) = 2.
%Y Cf. A103431, A103432, A106378, A106379, A106381, A106383.
%K nonn,more
%O 0,3
%A _Sven Simon_, Apr 30 2005
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