|
|
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.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|