A049036 - OEIS

A049036

Mean gap between successive primes up to k-th prime is an integer.

2, 10, 68, 438, 442, 2616, 100350, 100354, 100360, 637198, 637306, 27066970, 27067050, 27067102, 27067114, 27067116, 179992840, 179993002, 55762149072, 382465573492, 2636913002950

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..21.

Chris K. Caldwell, Prime Gaps.

FORMULA

k such that (k - 1) divides (prime(k) - k - 1), or equivalently,

K such that (k - 1) divides (prime(k) - 2).

a(n) = PrimePi(A049038(n)). - Amiram Eldar, Jul 17 2025

EXAMPLE

a(2) = 10 since 9 (number of gaps) divides 18 (number of composites less than 29, the 10th prime). Therefore the "average" gap less than 29 is exactly 2.

MATHEMATICA

Select[Range[2, 10^6], IntegerQ[(Prime[#]-2)/(#-1)] &] (* Stefano Spezia, Jul 17 2025 *)

CROSSREFS

Cf. A000720, A049038, A049066, A228543.

Sequence in context: A325995 A366178 A382617 * A208561 A152620 A152621

Adjacent sequences: A049033 A049034 A049035 * A049037 A049038 A049039

KEYWORD

nonn,more

AUTHOR

G. L. Honaker, Jr.

EXTENSIONS

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 25 2000

Three more terms from Phil Carmody, Jul 23 2003

STATUS

approved