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A319049
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Primes p such that none of p - 1, p - 2 and p - 3 are squarefree.
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3
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101, 127, 353, 727, 1277, 1423, 1451, 1667, 2153, 2351, 2647, 3187, 3251, 3511, 3701, 3719, 3727, 4421, 4951, 5051, 5393, 5527, 6427, 6653, 6959, 7517, 7867, 8527, 9127, 9551, 9803, 9851, 10243, 10253, 10487, 10831, 11273, 11351, 11777, 11827, 12007, 12251, 12277
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OFFSET
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1,1
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COMMENTS
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If p is a term, so that there are primes q,r,s such that q^2|p-3, r^2|p-2 and s^2|p-1, then the sequence includes all primes == p (mod q^2*r^2*s^2). In particular, the sequence is infinite, and a(n)/(n*log(n)) is bounded above and below by constants. - Robert Israel, Sep 09 2018
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LINKS
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EXAMPLE
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98 = 2*7^2, 99 = 3^2*11 and 100 = 2^2*5^2. So 101 is a term.
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MAPLE
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Res:= NULL: count:= 0:
p:= 1;
while count < 100 do
p:= nextprime(p);
if not ormap(numtheory:-issqrfree, [p-1, p-2, p-3]) then
count:= count+1; Res:= Res, p
fi
od:
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MATHEMATICA
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Select[Prime[Range[2000]], !SquareFreeQ[# - 1] && !SquareFreeQ[# - 2] && !SquareFreeQ[# - 3]&] (* Jean-François Alcover, Sep 17 2018 *)
Select[Prime[Range[1500]], NoneTrue[#-{1, 2, 3}, SquareFreeQ]&] (* Harvey P. Dale, Apr 11 2022 *)
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PROG
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(PARI) isok(p) = isprime(p) && !issquarefree(p-1) && !issquarefree(p-2) && !issquarefree(p-3); \\ Michel Marcus, Sep 09 2018
(Magma) [p: p in PrimesUpTo(13000) | not IsSquarefree(p-1) and not IsSquarefree(p-2) and not IsSquarefree(p-3)]; // Vincenzo Librandi, Sep 17 2018
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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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