OFFSET
1,1
COMMENTS
Conjecture: (1/2)(prime(x+1) + prime(x)) is not prime for all x.
This is obvious: (prime(x+1)+prime(x))/2 is strictly between prime(x) and prime(x+1), so if it were prime, prime(x+1) wouldn't be the next prime after prime(x). - Robert Israel, Feb 04 2019
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
Prime(2+1) + prime(2) = 5+3 = 8. 1/4(8) = 2. 2 is the first entry.
MAPLE
filter:= proc(t) local v; v:= (ithprime(t)+ithprime(t+1))/4; v::integer and isprime(v) end proc:
select(filter, [$1..2000]); # Robert Israel, Feb 04 2019
MATHEMATICA
Transpose[Select[Table[{i, Prime[i], Prime[i+1]}, {i, 1200}], PrimeQ[Total[Rest[#]]/4]&]][[1]](* Harvey P. Dale, Mar 24 2011 *)
Position[Partition[Prime[Range[1100]], 2, 1], _?(PrimeQ[Total[#]/4]&)]//Flatten (* Harvey P. Dale, Sep 11 2022 *)
PROG
(PARI) f(n) = for(x=1, n, y=prime(x+1)+prime(x); if(y%4==0 && isprime(y\4), print1(x", ")))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Sep 09 2004
STATUS
approved