The On-Line Encyclopedia of Integer Sequences (OEIS)

A240475 revision #17

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

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OFFSET

1,1

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.

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[Select[Partition[Select[Range[2000], SquareFreeQ], 3, 1], #[[3]]-#[[2]]==#[[2]]-#[[1]]&][[;; , 2]], 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

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

Sequence in context: A042925 A019413 A040138 * A107139 A042055 A075683

Adjacent sequences: A240472 A240473 A240474 * A240476 A240477 A240478

KEYWORD

nonn

AUTHOR

Chris Boyd, Apr 06 2014

STATUS

editing