

A268270


Least prime that is at distance > n from the nearest squarefree number.


0




OFFSET

0,1


LINKS



EXAMPLE

a(0)=2 is the least prime and it is at distance 1 from the nearest squarefree numbers (1 and/or 3).
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.
a(2)=727 is the least prime p such that p2 and p+1 are (two consecutive terms) in A068781, namely A068781(75..76).
a(3)=47527 is the least prime p such that p3 and p+1 are (two consecutive terms) in A070258, namely A070258(878..879).
a(4)=29002021 is the least prime p such that p4 and p+1 are (two consecutive terms) in A070284.
a(5)=494501773 is the least prime p such that p5 and p+1 are (two consecutive terms) in A078144.
Similarly, for n = 6, 7, 8 and 9, a(n) is the least prime p such that pn and p+1 are (two consecutive terms) in A049535, A077640, A077647 and A078143, respectively.


PROG

(PARI) a(n)=forprime(p=n, , for(s=1, n, (issquarefree(ps)issquarefree(p+s)) && next(2)); return(p))


CROSSREFS



KEYWORD

nonn,more,hard


AUTHOR



EXTENSIONS



STATUS

approved



