A091313 Smallest prime x > n such that x (mod n) = x (mod prime(n)).

2, 7, 17, 29, 59, 79, 239, 157, 211, 293, 347, 449, 541, 607, 709, 853, 1009, 1103, 1277, 1423, 1543, 1741, 1913, 2137, 2437, 2633, 2789, 2999, 3163, 3391, 3943, 4201, 4523, 4729, 5227, 5437, 5813, 6197, 6521, 6947, 7349, 7603, 8219, 8501, 8867, 9157, 9923

Offset

1,1

Comments

a(n) always exists, e.g. by Dirchlet's theorem on primes in arithmetic progressions there are infinitely many primes == 1 (mod n * prime(n)). - Robert Israel, Jun 05 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(2) = 7 because prime(2) = 3 and x = 7 is smallest prime > 2 such that x (mod 2) = x (mod 3).

Maple

f:= proc(n) local b, u, k, x;
   b:= ithprime(n);
   for u from 1 do
     for k from 1 to n-1 do
        x:= k + u*n*b;
        if isprime(x) then return x fi
   od od
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Jun 05 2025

Prog

(PARI) a(n) = {p = nextprime(n+1); while ( (p % n) != (p % prime(n)), p = nextprime(p+1)); p; } \\ Michel Marcus, Oct 05 2013

Crossrefs

Cf. A000040.

Sequence in context: A031377 A019357 A024920 * A049554 A019398 A086513

Adjacent sequences: A091310 A091311 A091312 * A091314 A091315 A091316

Keyword

nonn

Author

Zak Seidov, Feb 21 2004

Status

approved