A048198 Number of primes between successive n's, where n mod 10 = 5.

2, 3, 3, 2, 3, 2, 2, 3, 2, 1, 3, 3, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 3, 2, 1, 2, 2, 3, 1, 0, 3, 1, 1, 1, 3, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 1, 2, 0, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 2, 1, 1, 3, 0, 3, 1, 0, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 2, 1

Offset: 0

Author

Enoch Haga

Keywords

• easy
• nonn

Comments

A way to visualize the distribution of primes without the clutter of the numbers themselves. Consecutive 0's indicate stretches where there are no primes. Other patterns become obvious, as a string of 2's or 1's.

Examples

			Between n's 115 and 125 there are no primes, indicated by the entry 0.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A048199.

Programs

Maple

f:= n -> nops(select(isprime, [$10*n-4..10*n+4])):
map(f, [$0..100]); # Robert Israel, Nov 22 2018

Mathematica

a[n_] := Length[Select[Range[Max[10 n - 4, 1], 10 n + 4], PrimeQ]]; Array[a, 100, 0] (* Amiram Eldar, Nov 22 2018 *)
Join[{2},Differences[PrimePi[Range[5,1115,10]]]] (* Harvey P. Dale, Jul 20 2023 *)

PARI

a(n) = my(na = 10*n - 5); my(nb = na + 10); primepi(nb - 1) - primepi(na + 1); \\ Michel Marcus, Aug 25 2013

Formula

Starting at 0, count primes between 0-5, 5-15, 15-25, etc.