OFFSET
1,1
COMMENTS
a(8) and higher do not exist because at least one of p+2, p+4, ..., p+16 is divisible by 9 unless p is divisible by 9, in which case it is not prime. - Charles R Greathouse IV, Apr 27 2015
EXAMPLE
a(1) = 3 because 3 + 1 = 4 is not squarefree, 3 + 2 = 5 is squarefree, 3 is prime.
MAPLE
p:= 0:
for i from 1 to 5000 do
p:= nextprime(p);
for n from 1 while numtheory:-issqrfree(p+2*n)
and not numtheory:-issqrfree(p+2*n-1) do
if not assigned(A[n]) then A[n]:= p
fi
od:
od:
seq(A[i], i=1..7); # Robert Israel, Apr 27 2015
MATHEMATICA
a[n_] := For[k=1, True, k++, p = Prime[k]; r = p + Range[1, 2*n-1, 2]; If[(And @@ ((!SquareFreeQ[#])& /@ r)) && And @@ (SquareFreeQ /@ (r+1)), Return[p]]]; Table[ a[n], {n, 1, 7}] (* Jean-François Alcover, Apr 28 2015 *)
PROG
(PARI) has(p, n)=for(i=1, 2*n, if(issquarefree(p+i)==i%2, return(0))); 1
a(n)=forprime(p=2, , if(has(p, n), return(p))) \\ Charles R Greathouse IV, Apr 27 2015
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Juri-Stepan Gerasimov, Apr 25 2015
EXTENSIONS
a(3) corrected, a(6)-a(7) added by Charles R Greathouse IV, Apr 27 2015
STATUS
approved