A086708 Primes p such that p-1 and p+1 are both divisible by cubes.

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

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