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A086708 Primes p such that p-1 and p+1 are both divisible by cubes. 9
271, 487, 593, 751, 809, 919, 1249, 1567, 1783, 1889, 1999, 2647, 2663, 2753, 2969, 3079, 3511, 3617, 3727, 3833, 3943, 4049, 4159, 4481, 4591, 4751, 4801, 5023, 6857, 6967, 7937, 8263, 8369, 9127, 9343, 10289, 10313, 10529, 10639, 11071, 11177 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

{p in A000040: p+1 in A046099 and p-1 in A046099}. - R. J. Mathar, Dec 08 2015

A089199 INTERSECT A089200. - R. J. Mathar, Dec 08 2015

MAPLE

isA086708 := proc(n)

    if isprime(n) then

        isA046099(n-1) and isA046099(n+1) ;

    else

        false;

    end if;

end proc:

n := 1:

for c from 1 to 50000 do

    if isA086708(c) then

        printf("%d %d\n", n, c) ;

        n := n+1 ;

    end if;

end do: # R. J. Mathar, Dec 08 2015

Res:= NULL: count:= 0:

p:= 1:

while count < 100 do

  p:= nextprime(p);

  if max(seq(t[2], t=ifactors(p-1)[2]))>=3 and max(seq(t[2], t=ifactors(p+1)[2]))>=3 then

    count:= count+1; Res:= Res, p;

  fi

od:

Res; # Robert Israel, Jul 11 2018

MATHEMATICA

f[n_]:=Max[Last/@FactorInteger[n]]; lst={}; Do[p=Prime[n]; If[f[p-1]>=3&&f[p+1]>=3, AppendTo[lst, p]], {n, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 03 2009 *)

PROG

(PARI)

\\ Input no. of iterations n, power p and number to subtract and add k.

powerfreep4(n, p, k) = { c=0; pc=0; forprime(x=2, n, pc++; if(!ispowerfree(x-k, p) && !ispowerfree(x+k, p), c++; print1(x", "); ) ); print(); print(c", "pc", "c/pc+.0) }

ispowerfree(m, p1) = { flag=1; y=component(factor(m), 2); for(i=1, length(y), if(y[i] >= p1, flag=0; break); ); return(flag) } \\ Cino Hilliard, Dec 08 2003

CROSSREFS

Cf. A162870 (subsequence).

Sequence in context: A142762 A141029 A090838 * A142637 A288881 A245969

Adjacent sequences:  A086705 A086706 A086707 * A086709 A086710 A086711

KEYWORD

nonn

AUTHOR

Jason Earls and Amarnath Murthy, Jul 28 2003

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)