A228543 - OEIS

A228543

a(n) is the integer-valued average gap between successive primes from prime(1) to prime(k(n)), where k(n) = A049036(n).

1, 3, 5, 7, 7, 9, 13, 13, 13, 15, 15, 19, 19, 19, 19, 19, 21, 21, 27, 29, 31

OFFSET

1,2

COMMENTS

a(n) arises from A049036 and A049038.

LINKS

FORMULA

a(n) = (A049038(n)-2)/(A049036(n)-1).

a(n) = A049066(n) + 1. - Amiram Eldar, Jul 17 2025

EXAMPLE

For n = 1 a(n) = (prime(k(1))-2)/(k(1)-1), where k(1) = 2, p(2) = 3, and a(1) = 1.

For n = 2 a(n) = (prime(k(2))-2)/(k(2)-1), where k(2) = 10, p(10) = 29, and a(2) = 3.

For n = 3 a(n) = (prime(k(3))-2)/(k(3)-1), where k(3) = 68, p(68) = 337, and a(3) = 5.

MATHEMATICA

a = {}; Do[s = (Prime[k] - 2)/(k - 1); If[IntegerQ[s], AppendTo[a, s]], {k, 2, 1000000000}]; a

CROSSREFS

KEYWORD

nonn,more

AUTHOR

V.J. Pohjola, Aug 25 2013

STATUS

approved