A240475 Primes that are midway between the closest flanking squarefree numbers.

2, 17, 19, 53, 89, 163, 197, 199, 233, 251, 269, 271, 293, 307, 337, 379, 449, 487, 491, 521, 557, 593, 631, 701, 739, 751, 809, 811, 881, 883, 919, 953, 991, 1013, 1049, 1061, 1063, 1097, 1151, 1171, 1279, 1459, 1471, 1493, 1531, 1549, 1567, 1601, 1637

Offset: 1

Author

Chris Boyd, Apr 06 2014

Keywords

• nonn

Comments

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

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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", ")))