A088573 Smallest m such that {n+k*(n-1): 0<k<=m} contains exactly as many primes as <= n.

1, 1, 2, 3, 6, 7, 5, 15, 10, 11, 9, 29, 12, 33, 13, 15, 21, 35, 14, 57, 20, 25, 27, 43, 18, 45, 22, 29, 26, 59, 19, 81, 35, 39, 29, 65, 27, 87, 41, 47, 39, 89, 24, 95, 52, 55, 42, 103, 36, 117, 37, 59, 48, 131, 36, 89, 49, 85, 68, 109, 38, 131, 67, 85, 69, 103, 45

Offset

1,3

Comments

#{p prime: p=n+k*(n-1) and 0<k<=a(n)} = A000720(n).

Links

Table of n, a(n) for n=1..67.

Index entries for sequences related to primes in arithmetic progressions

Eric Weisstein's World of Mathematics, Dirichlet's Theorem

Example

n=7: #{primes<=7} = #{2,3,5,7} = 4, first 4 primes of the form
7+k*(7-1): 13=7+1*6, 19=7+2*6, 31=7+4*6 and 37=7+5*6: a(7)=5.

Crossrefs

Sequence in context: A191726 A234025 A245444 * A181514 A225755 A126388

Adjacent sequences: A088570 A088571 A088572 * A088574 A088575 A088576

Keyword

nonn

Author

Reinhard Zumkeller, Nov 18 2003

Status

approved