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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A002145 corresponds to the natural numbers that are also Gaussian prime numbers.
This sequence generalizes to Gaussian integers an idea developed in A308261.
Visually, the connected components of G appear like constellations (see representation in Links section).
LINKS
Eric Weisstein's World of Mathematics, Gaussian Prime
EXAMPLE
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.
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A115020 A169735 A096582 * A220023 A115048 A112525
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 15 2019
STATUS
approved

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Last modified June 20 13:44 EDT 2024. Contains 373527 sequences. (Running on oeis4.)