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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 Seiichi Manyama, Table of n, a(n) for n = 1..10000 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 *) 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 Cf. A000040, A039787, A049231, A240473, A257545, A318959. Sequence in context: A095635 A060916 A075793 * A052086 A154270 A056730 Adjacent sequences:  A319046 A319047 A319048 * A319050 A319051 A319052 KEYWORD nonn AUTHOR Seiichi Manyama, Sep 08 2018 STATUS approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)