A340752 a(n) is the least prime p such that there is at least one prime <= p in each congruence class mod prime(n).

3, 7, 19, 29, 43, 103, 103, 191, 137, 317, 311, 439, 379, 463, 967, 607, 709, 1061, 1013, 829, 1021, 1319, 1201, 1493, 1499, 2143, 1973, 2459, 2333, 2203, 3697, 3089, 3923, 2909, 3449, 4517, 3539, 4451, 3923, 4801, 4007, 4799, 4793, 3727, 5651, 4349, 5591, 4793, 6581, 8059, 6043, 9769, 5507, 6997

Offset

1,1

Comments

a(n) is the maximum of row n of A340753.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

a(3) = 19 because with prime(3)=5, the first primes in each congruence class are 5 == 0 (mod 5), 11 == 1 (mod 5), 2 == 2 (mod 5), 3 == 3 (mod 5), and 19 == 4 (mod 5), and the maximum of these is 19.

Maple

g:= proc(p) local S, q;
  S:= {$0..p-1};
  q:= 1;
  while S <> {} do
    q:= nextprime(q);
    S:= S minus {q mod p};
  od;
  q
end proc:
seq(g(ithprime(i)), i=1..100);

Crossrefs

Cf. A340753.

Sequence in context: A239219 A056725 A091738 * A360228 A358238 A136054

Adjacent sequences: A340749 A340750 A340751 * A340753 A340754 A340755

Keyword

nonn

Author

Robert Israel, Jan 19 2021

Status

approved