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A319049 Primes p such that none of p - 1, p - 2 and p - 3 are squarefree. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
EXAMPLE
98 = 2*7^2, 99 = 3^2*11 and 100 = 2^2*5^2. So 101 is a term.
MAPLE
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:
Res; # Robert Israel, Sep 09 2018
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A095635 A060916 A075793 * A052086 A154270 A056730
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 08 2018
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)