%I #28 Jan 02 2023 12:30:52
%S 2,17,727,47527,29002021,494501773,44633461423,7489886099881
%N Least prime that is at distance > n from the nearest squarefree number.
%H Chris Thompson, <a href="http://list.seqfan.eu/oldermail/seqfan/2016-January/015969.html">What is the next one? [primes isolated from squarefrees]</a>, SeqFan list.
%e a(0)=2 is the least prime and it is at distance 1 from the nearest squarefree numbers (1 and/or 3).
%e a(1)=17 is the least prime that has no squarefree neighbor: both 16 and 18 are divisible by a square; the nearest squarefree numbers, 15 and 19, are both at distance 2.
%e a(2)=727 is the least prime p such that p-2 and p+1 are (two consecutive terms) in A068781, namely A068781(75..76).
%e a(3)=47527 is the least prime p such that p-3 and p+1 are (two consecutive terms) in A070258, namely A070258(878..879).
%e a(4)=29002021 is the least prime p such that p-4 and p+1 are (two consecutive terms) in A070284.
%e a(5)=494501773 is the least prime p such that p-5 and p+1 are (two consecutive terms) in A078144.
%e Similarly, for n = 6, 7, 8 and 9, a(n) is the least prime p such that p-n and p+1 are (two consecutive terms) in A049535, A077640, A077647 and A078143, respectively.
%o (PARI) a(n)=forprime(p=n,,for(s=1,n,(issquarefree(p-s)||issquarefree(p+s)) && next(2)); return(p))
%Y Cf. A023186, A045882.
%K nonn,more,hard
%O 0,1
%A _Juri-Stepan Gerasimov_ and _M. F. Hasler_, Jan 01 2016
%E a(4) corrected and a(5) computed by _Christopher E. Thompson_, Jan 20 2016
%E a(6)-a(7) from _Bert Dobbelaere_, Jan 28 2019