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A185271 Differences between consecutive norms of Gaussian primes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..75.

Wikipedia, Gaussian Integer

Eric W. Weisstein, MathWorld: Gaussian Prime

Eric W. Weisstein, MathWorld: Moat-Crossing Problem

Index entries for Gaussian integers and primes

FORMULA

a(n) = b(n+1) - b(n) where b(n) = sequence A055025.

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: A112180 A058559 A232092 * A158012 A032446 A271563

Adjacent sequences:  A185268 A185269 A185270 * A185272 A185273 A185274

KEYWORD

nonn,easy

AUTHOR

Patrick P Sheehan, Jan 25 2012

STATUS

approved

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Last modified March 21 10:13 EDT 2019. Contains 321368 sequences. (Running on oeis4.)