

A163849


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


1



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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A111252, A145446.
Sequence in context: A095316 A095313 A095285 * A124591 A164837 A069675
Adjacent sequences: A163846 A163847 A163848 * A163850 A163851 A163852


KEYWORD

nonn,easy


AUTHOR

Vladimir Joseph Stephan Orlovsky, Aug 05 2009


EXTENSIONS

Edited by R. J. Mathar, Aug 12 2009


STATUS

approved



