%I #20 Jul 27 2024 16:13:34

%S 2,17,19,53,89,163,197,199,233,251,269,271,293,307,337,379,449,487,

%T 491,521,557,593,631,701,739,751,809,811,881,883,919,953,991,1013,

%U 1049,1061,1063,1097,1151,1171,1279,1459,1471,1493,1531,1549,1567,1601,1637

%N Primes that are midway between the closest flanking squarefree numbers.

%C Primes for which the corresponding A240473(m) is equal to A240474(m).

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

%C Primes equal to the average of three consecutive squarefree numbers.

%C 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.

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

%H Chris Boyd, <a href="/A240475/b240475.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%t Select[Mean/@Partition[Select[Range[2000],SquareFreeQ],3,1],PrimeQ] (* _Harvey P. Dale_, Jul 27 2024 *)

%o (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", ")))

%Y Cf. A000040, A075430, A075432, A166003, A176141, A240473, A240474, A240476.

%K nonn

%O 1,1

%A _Chris Boyd_, Apr 06 2014