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Differences between consecutive norms of Gaussian primes.
1

%I #21 Jul 19 2020 04:06:40

%S 3,4,4,4,12,8,4,8,4,8,12,16,8,4,8,4,8,16,12,8,16,8,12,4,32,4,8,16,12,

%T 8,4,12,20,4,20,12,4,8,12,16,8,4,8,12,12,16,8,4,48,12,8,12,16,12,8,16,

%U 8,12,4,24,12,8,12,4,24,8,24,24,4,8,4,24,12,12,8

%N Differences between consecutive norms of Gaussian primes.

%C If this sequence goes to infinity fast enough then the Gaussian moat-crossing problem is solved and it is impossible to walk to infinity in the complex plane using steps of bounded length stepping only on Gaussian primes.

%H Amiram Eldar, <a href="/A185271/b185271.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/GaussianPrime.html">MathWorld: Gaussian Prime</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Moat-CrossingProblem.html">MathWorld: Moat-Crossing Problem</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gaussian_integer">Gaussian Integer</a>

%H <a href="https://oeis.org/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>

%F a(n) = A055025(n+1) - A055025(n).

%e The first Gaussian prime (restricting ourselves to the first octant) is 1+i which has norm 2 (1^2+1^2). The second is 2+i with norm 5 (2^2+1^2). The difference in those norms is 3, the first term in this sequence.

%Y Cf. A055025 (norms of Gaussian primes).

%K nonn,easy

%O 1,1

%A _Patrick P Sheehan_, Jan 25 2012