This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
3, 127, 24391, 29789, 328511, 2460373, 3048623, 9393929, 10503461 (list; graph; refs; listen; history; text; internal format)



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.


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


p=3 is in the sequence because the distance p-1=2 to the cube 1^3 below 3, and also the distance 8-p=5 to the cube 8=2^3 above p are prime.

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


Clear[f, lst, p, n]; f[n_]:=IntegerPart[n^(1/3)]; lst={}; Do[p=Prime[n]; If[PrimeQ[p-f[p]^3]&&PrimeQ[(f[p]+1)^3-p], AppendTo[lst, p]], {n, 9!}]; lst

dncQ[n_]:=Module[{c=Floor[Surd[n, 3]]}, AllTrue[{n-c^3, (c+1)^3-n}, PrimeQ]]; Select[Prime[Range[230000]], dncQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 16 2016 *)


Cf. A163848

Sequence in context: A071151 A041867 A134711 * A258671 A243213 A264582

Adjacent sequences:  A163847 A163848 A163849 * A163851 A163852 A163853




Vladimir Joseph Stephan Orlovsky, Aug 05 2009


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)