A163849 Primes p such that the difference between the nearest cubes above and below p is prime.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 733, 739, 743, 751, 757, 761, 769, 773

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 05 2009

Keywords

• nonn
• easy

Comments

There is a sequence A048763(A000040(n)) = A145446(n) of nearest cubes above the primes and a sequence A048762(A000040(n)) of nearest cubes below the primes.

If the difference A145446(n) - A048762(A000040(n)) is prime, then A000040(n) is in this sequence.

Examples

			The difference of cubes 6^3 - 5^3 = 91 = 7*13 is not prime, so the primes larger than 5^3 = 125 but smaller than 6^3 = 216 are not in the sequence.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A111252, A145446.

Programs

Mathematica

f[n_]:=IntegerPart[n^(1/3)]; lst={};Do[p=Prime[n];If[PrimeQ[(f[p]+1)^3-f[p]^3], AppendTo[lst,p]],{n,6!}];lst

Extensions

Edited by R. J. Mathar, Aug 12 2009