A162989 Lesser of twin primes p such that none of p-1, p+1 and p+3 are cubefree.

69497, 416501, 474497, 632501, 960497, 1068497, 1226501, 1402871, 1464101, 1635497, 1716497, 1919429, 1986497, 2114249, 2144501, 2283497, 2645189, 3120497, 3174497, 3232751, 3305501, 3332501, 3525497, 3637169, 3998537

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

p=69497 and p+2=69499 are twin primes, also:
p-1=69496=2^3*7*17*73
p+1=69498=2*3^5*11*13
p+3=69500=2^2*5^3*139.

Maple

cf:= proc(n) local F;
    F:= ifactors(n)[2];
    max(map(t->t[2], F))>=3
end proc:
select(t -> isprime(t) and isprime(t+2) and cf(t-1) and cf(t+1) and cf(t+3), [seq(i, i=5..10^7, 6)]); # Robert Israel, Nov 24 2020

Mathematica

f[m_]:=Max[Last/@FactorInteger[m]]>=3;
S={}; Do[If[PrimeQ[p=6x-1]&&PrimeQ[p+2]&&
f[p-1]==f[p+1]==f[p+3]==True, AppendTo[S, p]], {x, 1, 10^6}]; S

Crossrefs

Cf. A046099.

See A162874 for another version.

Sequence in context: A205758 A205588 A162874 * A052195 A089218 A224324

Adjacent sequences: A162986 A162987 A162988 * A162990 A162991 A162992

Keyword

nonn

Author

Zak Seidov, Jul 19 2009

Extensions

Definition clarified by Robert Israel, Nov 24 2020

Status

approved