A106385 - OEIS

%I #6 Mar 31 2012 10:28:43

%S 1,2,3,1,191

%N 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 a, as defined in A103431. The sum of these primes up to a+bi is divisible by a+bi. a(n) is the real part a of such a+bi.

%C A106386 has the imaginary parts.

%H Sven Simon, <a href="/A106385/a106385.txt">Table of n, a(n), A106385(n), a+b*i and the associated partial sum of A103431</a>

%e (1+i)+(1+2i)+(2+i)+3+(2+3i)+(3+2i)+(1+4i)+(4+i)+(2+5i)+(5+2i)+(1+6i)+(6+i)+(4+5i)+

%e (5+4i)+7+(2+7i)+(7+2i)+(5+6i)+(6+5i)+(3+8i) = (70+65i), (70+65i) / (3+8i) = (10-5i).

%e This is the third number with the property, so a(3)=3.

%Y Cf. A103431, A103432, A106386.

%K nonn

%O 1,2

%A _Sven Simon_, Apr 30 2005