A386268 a(n) = numerator((prime(n) - 2)/(n - 1)).

1, 3, 5, 9, 11, 5, 17, 21, 3, 29, 35, 13, 41, 45, 17, 57, 59, 65, 69, 71, 11, 81, 87, 95, 99, 101, 35, 107, 111, 25, 129, 135, 137, 147, 149, 155, 161, 165, 57, 177, 179, 9, 191, 195, 197, 209, 221, 75, 227, 231, 79, 239, 249, 85, 261, 267, 269, 275, 279, 281

Offset

2,2

Comments

a(n)/A386269(n) is the average distance between the first n primes.

References

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Exercise 3.6.6 on page 120.

Links

Stefano Spezia, Table of n, a(n) for n = 2..10000

Formula

a(n)/A386269(n) ~ log(n).

Mathematica

a[n_]:=Numerator[(Prime[n]-2)/(n-1)]; Array[a, 60, 2]

Crossrefs

Cf. A000040, A049036, A049038, A228543, A386269 (denominators).

Sequence in context: A385227 A385164 A270780 * A304251 A379915 A309135

Adjacent sequences: A386265 A386266 A386267 * A386269 A386270 A386271

Keyword

nonn,easy,frac

Author

Stefano Spezia, Jul 17 2025

Status

approved