A071220 Numbers n such that prime(n) + prime(n+1) is a cube.

2, 28, 1332, 3928, 16886, 157576, 192181, 369440, 378904, 438814, 504718, 539873, 847252, 1291597, 1708511, 1837979, 3416685, 3914319, 5739049, 6021420, 7370101, 7634355, 8608315, 9660008, 10378270, 14797144, 15423070, 18450693

Offset: 1

Author

Labos Elemer, May 17 2002

Keywords

• nonn

Comments

The corresponding primes are in A061308; n^3 is a sum of two successive primes in A074925.

Prime(n)+ Prime(n+1) is a square in A064397; n^2 is a sum of two successive primes in A074924;

Examples

			28 is in the list because prime(28)+prime(29) = 107+109 =216 = 6^3.
n=1291597: prime(1291597)+prime(1291598) = 344*344*344.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A064397, A074925, A074924, A001043.

Programs

Mathematica

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; Do[ If[ n^3 == PrevPrim[Floor[(n^3)/2]] + NextPrim[Floor[(n^3)/2]], Print[ PrimePi[ Floor[(n^3)/2]]]], {n, 2, 10^4}]
Flatten[Position[Total/@Partition[Prime[Range[20000000]],2,1],?(IntegerQ[ Surd[ #,3]]&)]] (* _Harvey P. Dale, May 28 2014 *)

Python

from _future_ import division
from sympy import isprime, prevprime, nextprime, primepi
A071220_list, i = [], 2
while i < 10**6:
    n = i**3
    m = n//2
    if not isprime(m) and prevprime(m) + nextprime(m) == n:
        A071220_list.append(primepi(m))
    i += 1 # Chai Wah Wu, May 31 2017

Formula

A001043(x)=m^3 for some m; if p(x+1)+p(x) is a cube, then x is here.

a(n) = primepi(A061308(n)). - Michel Marcus, Oct 24 2014

Extensions

Edited and extended by Robert G. Wilson v, Oct 07 2002