A268270 Least prime that is at distance > n from the nearest squarefree number.

2, 17, 727, 47527, 29002021, 494501773, 44633461423, 7489886099881

Offset

0,1

Links

Table of n, a(n) for n=0..7.

Chris Thompson, What is the next one? [primes isolated from squarefrees], SeqFan list.

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 p-2 and p+1 are (two consecutive terms) in A068781, namely A068781(75..76).
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).
a(4)=29002021 is the least prime p such that p-4 and p+1 are (two consecutive terms) in A070284.
a(5)=494501773 is the least prime p such that p-5 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 p-n 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(p-s)||issquarefree(p+s)) && next(2)); return(p))

Crossrefs

Cf. A023186, A045882.

Sequence in context: A013063 A012992 A054867 * A167436 A015189 A012944

Adjacent sequences: A268267 A268268 A268269 * A268271 A268272 A268273

Keyword

nonn,more,hard

Author

Juri-Stepan Gerasimov and M. F. Hasler, Jan 01 2016

Extensions

a(4) corrected and a(5) computed by Christopher E. Thompson, Jan 20 2016

a(6)-a(7) from Bert Dobbelaere, Jan 28 2019

Status

approved