A185271 Differences between consecutive norms of Gaussian primes.

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, 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, 8, 12, 4, 24, 12, 8, 12, 4, 24, 8, 24, 24, 4, 8, 4, 24, 12, 12, 8

Offset

1,1

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric W. Weisstein, MathWorld: Gaussian Prime

Eric W. Weisstein, MathWorld: Moat-Crossing Problem

Wikipedia, Gaussian Integer

Index entries for Gaussian integers and primes

Formula

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

Example

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.

Crossrefs

Cf. A055025 (norms of Gaussian primes).

Sequence in context: A058559 A232092 A345196 * A352285 A158012 A032446

Adjacent sequences: A185268 A185269 A185270 * A185272 A185273 A185274

Keyword

nonn,easy

Author

Patrick P Sheehan, Jan 25 2012

Status

approved