A257545 a(0) = 2, a(n) = smallest prime p such that none of p - 1, p - 2,... p - n are squarefree.

2, 5, 29, 101, 5051, 5051, 73453, 671353, 130179187, 211014929, 262315477, 3639720053

Offset: 0

Author

Juri-Stepan Gerasimov, Apr 29 2015

Keywords

• nonn
• more

Examples

			a(3) = 101 because 101 is prime and none of 101 - 1 = 100, 101 - 2 = 99, and 101 - 3 = 98 are squarefree.
		

Crossrefs

Cf. A257108.

Programs

Maple

p:= 2:
A[0]:= 2:
m:= 0:
while p < 10^6 do
p:= nextprime(p);
for k from 1 while not numtheory:-issqrfree(p-k) do od:
if k > m+1 then
   for j from m+1 to k-1 do A[j]:= p od:
   m:= k-1;
fi
od:
seq(A[i],i=0..m); # Robert Israel, Apr 29 2015

PARI

a(n)=forprime(p=2,,for(k=1,n,if(issquarefree(p-k), next(2))); return(p)) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) << A002110(n)^10 by the CRT and Xylouris' improvement to Linnik's theorem. - Charles R Greathouse IV, Apr 29 2015

Extensions

a(9)-a(11) from Charles R Greathouse IV, Apr 29 2015