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A240475
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Primes that are midway between the closest flanking squarefree numbers.
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6
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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
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Mean/@Partition[Select[Range[2000], SquareFreeQ], 3, 1], PrimeQ] (* Harvey P. Dale, Jul 27 2024 *)
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PROG
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(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", ")))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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