OFFSET

1,1

COMMENTS

Primes equal to the average of the closest flanking squarefree numbers.

Primes equal to the average of three consecutive squarefree numbers.

Most terms are such that a(n)+2 and a(n)-2 are the closest squarefree numbers. The first term > 2 for which this is not the case is a(880) = 47527.

494501773, 765921647, 930996623 are the terms < 10^9 that also belong to A176141.

LINKS

Chris Boyd, Table of n, a(n) for n = 1..10000

EXAMPLE

19 is a term because it is midway between the closest flanking squarefree numbers 17 and 21.

On the other hand, 29 is not a term because it is not midway between the closest flanking squarefree numbers 26 and 30.

MATHEMATICA

Select[Mean/@Partition[Select[Range[2000], SquareFreeQ], 3, 1], PrimeQ] (* Harvey P. Dale, Jul 27 2024 *)

PROG

(PARI) forprime(p=1, 1650, forstep(j=p-1, 1, -1, if(issquarefree(j), L=j; break)); for(j=p+1, 2*p, if(issquarefree(j), G=j; break)); if(G-p==p-L, print1(p", ")))

CROSSREFS

KEYWORD

nonn

AUTHOR

Chris Boyd, Apr 06 2014

STATUS

approved