A308660 For any Gaussian integer z, let d(z) be the distance from z to the nearest Gaussian prime distinct from z; we build an undirected graph G on top of the Gaussian prime numbers as follows: two Gaussian prime numbers p and q are connected iff at least one of d(p) or d(q) equals the distance from p to q; a(n) is the number of elements in the connected component of G containing A002145(n).
100, 100, 3, 3, 3, 15, 48, 48, 9, 19, 5, 18, 18, 3, 17, 7, 41, 7, 17, 3, 3, 3, 9, 31, 3, 6, 6, 3, 11, 33, 3, 3, 9, 5, 13, 3, 15, 7, 23, 7, 3, 3, 3, 3, 5, 3, 13, 3, 3, 5, 11, 15, 3, 9, 3, 25, 19, 29, 23, 13, 3, 3, 5, 5, 3, 7, 15, 3, 25, 3, 7, 5, 3, 5, 3, 3, 3
Offset: 1
Keywords
Examples
For n=3: - A002145(3) = 11, - the nearest Gaussian primes to 11 (at equal distance) are 10+i and 10-i, - the other Gaussian primes around 11, 10+i and 10-i are nearer from other Gaussian primes, - so the connected component containing 11 contains: 11, 10+i and 10-i, - and a(3) = 3.
Links
- Rémy Sigrist, Representation of the connected components of G with a term z such that 0 <= Re(z) <= 100 and 0 <= Im(z) <= 100
- Rémy Sigrist, PARI program for A308660
- Eric Weisstein's World of Mathematics, Gaussian Prime
Programs
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PARI
See Links section.
Comments