login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071220 Numbers n such that prime(n) + prime(n+1) is a cube. 5
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

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

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

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

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

CROSSREFS

Cf. A064397, A074925, A074924, A001043.

Sequence in context: A009674 A143598 A324077 * A063794 A238817 A202942

Adjacent sequences:  A071217 A071218 A071219 * A071221 A071222 A071223

KEYWORD

nonn

AUTHOR

Labos Elemer, May 17 2002

EXTENSIONS

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

STATUS

approved

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 September 19 23:31 EDT 2019. Contains 327207 sequences. (Running on oeis4.)