

A163850


Primes p such that their distance to the nearest cube above p and also their distance to the nearest cube below p are prime.


0




OFFSET

1,1


COMMENTS

The two sequences A048763(p) and A048762(p), p=A000040(n), define
nearest cubes above and below each prime p. If p is in A146318, the
distance to the larger cube, A048763(p)p, is prime. If p is
in the set {3, 11, 13, 19, 29, 67,...,107, 127, 223,..}, the distance to the lower
cube is prime. If both of these distances are prime, we insert p into the sequence.


LINKS

Table of n, a(n) for n=1..9.


EXAMPLE

p=3 is in the sequence because the distance p1=2 to the cube 1^3 below 3, and also the distance 8p=5 to the cube 8=2^3 above p are prime.
p=127 is in the sequence because the distance p125=2 to the cube 125=5^3 below p, and also the distance 216p=89 to the cube 216=6^3 above p, are prime.


MATHEMATICA

Clear[f, lst, p, n]; f[n_]:=IntegerPart[n^(1/3)]; lst={}; Do[p=Prime[n]; If[PrimeQ[pf[p]^3]&&PrimeQ[(f[p]+1)^3p], AppendTo[lst, p]], {n, 9!}]; lst
dncQ[n_]:=Module[{c=Floor[Surd[n, 3]]}, AllTrue[{nc^3, (c+1)^3n}, PrimeQ]]; Select[Prime[Range[230000]], dncQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 16 2016 *)


CROSSREFS

Cf. A163848
Sequence in context: A071151 A041867 A134711 * A258671 A243213 A264582
Adjacent sequences: A163847 A163848 A163849 * A163851 A163852 A163853


KEYWORD

nonn


AUTHOR

Vladimir Joseph Stephan Orlovsky, Aug 05 2009


EXTENSIONS

Edited, first 5 entries checked by R. J. Mathar, Aug 12 2009
Two more terms (a(8) and a(9)) from Harvey P. Dale, Oct 16 2016


STATUS

approved



