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A303214
Prime numbers whose average with the previous prime is not divisible by 2 or 3.
1
3, 211, 223, 479, 521, 631, 673, 809, 1009, 1213, 1249, 1319, 1471, 1511, 1523, 1543, 1693, 1721, 1801, 1823, 1901, 2081, 2111, 2203, 2309, 2411, 2459, 2591, 2633, 2789, 2939, 3061, 3079, 3181, 3203, 3271, 3343, 3359, 3511, 3571, 3671, 3943, 4001, 4091, 4111
OFFSET
1,1
COMMENTS
Very similar to A031931.
3 and all prime(k+1) such that A001223(k) is divisible by 12. - Robert Israel, Jul 04 2018
LINKS
FORMULA
2 NOT(|) (p+previous_prime(p))/2 AND 3 NOT(|) (p+previous_prime(p))/2
EXAMPLE
p = 223 => (p + previous_prime(p))/2 = (223 +211)/2 = 7*31;
p = 53 => (p + previous_prime(p))/2 = (53 + 51)/2 = 52 (divisible by 2).
MAPLE
count:= 1: Res:= 3:
p:= 3:
while count < 100 do
q:= p; p:= nextprime(p);
v:= (q+p)/2;
if igcd(v, 6)=1 then
count:= count+1;
Res:= Res, p;
fi
od:
Res; # Robert Israel, Jul 04 2018
PROG
(PARI) ok(n)={my(t=n+precprime(n-1)); n > 2 && isprime(n) && t%4 && t%3} \\ Andrew Howroyd, Jul 02 2018
CROSSREFS
Sequence in context: A251864 A349073 A063407 * A258110 A072196 A038785
KEYWORD
nonn
AUTHOR
Olivier Bélot, Apr 19 2018
STATUS
approved