|
|
A071220
|
|
Numbers n such that prime(n) + prime(n+1) is a cube.
|
|
6
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
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;
|
|
LINKS
|
|
|
FORMULA
|
A001043(x)=m^3 for some m; if p(x+1)+p(x) is a cube, then x is here.
|
|
EXAMPLE
|
28 is in the list because prime(28)+prime(29) = 107+109 =216 = 6^3.
n=1291597: prime(1291597)+prime(1291598) = 344*344*344.
|
|
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 *)
|
|
PROG
|
(Python)
from __future__ import division
from sympy import isprime, prevprime, nextprime, primepi
while i < 10**6:
n = i**3
m = n//2
if not isprime(m) and prevprime(m) + nextprime(m) == n:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|