A356403 a(n) is the first prime p such that the average of p and the next n-1 primes congruent to p (mod n) is a prime.

5, 17, 11, 19, 11, 7, 5, 3, 3, 13, 3, 23, 7, 3, 29, 5, 3, 127, 17, 7, 7, 7, 31, 79, 5, 17, 3, 17, 37, 7, 23, 5, 3, 5, 17, 17, 11, 3, 5, 107, 23, 23, 7, 7, 11, 11, 5, 37, 11, 7, 3, 19, 37, 47, 37, 101, 11, 71, 5, 151, 13, 23, 3, 23, 3, 71, 11, 11, 29, 13, 3, 7, 97, 5, 47, 17, 3, 19, 11, 83, 17, 11

Offset

3,1

Links

Robert Israel, Table of n, a(n) for n = 3..10000

Example

a(4) = 19 because 19 is prime, the next 3 primes == 19 (mod 4) are 23, 31 and 43, and (19+23+31+43)/4 = 29 is prime.

Maple

f:= proc(n) local p, q, k, s, count;
  p:= 1;
  do
     p:= nextprime(p);
     if n mod p = 0 then next fi;
     s:= p; count:= 1;
     for q from p+n by n while count < n do
       if isprime(q) then s:= s+q; count:= count+1 fi
     od;
     if isprime(s/n) then return p fi
  od
end proc:
map(f, [$3..100]);

Crossrefs

Cf. A356383.

Sequence in context: A286816 A276831 A180024 * A178197 A302159 A070848

Adjacent sequences: A356400 A356401 A356402 * A356404 A356405 A356406

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Aug 05 2022

Status

approved