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

%I A071220 #17 May 31 2017 22:54:39
%S A071220 2,28,1332,3928,16886,157576,192181,369440,378904,438814,504718,
%T A071220 539873,847252,1291597,1708511,1837979,3416685,3914319,5739049,
%U A071220 6021420,7370101,7634355,8608315,9660008,10378270,14797144,15423070,18450693
%N A071220 Numbers n such that prime(n) + prime(n+1) is a cube.
%C A071220 The corresponding primes are in A061308; n^3 is a sum of two successive primes in A074925.
%C A071220 Prime(n)+ Prime(n+1) is a square in A064397; n^2 is a sum of two successive primes in A074924;
%H A071220 Chai Wah Wu, <a href="/A071220/b071220.txt">Table of n, a(n) for n = 1..1000</a>
%F A071220 A001043(x)=m^3 for some m; if p(x+1)+p(x) is a cube, then x is here.
%F A071220 a(n) = primepi(A061308(n)). - _Michel Marcus_, Oct 24 2014
%e A071220 28 is in the list because prime(28)+prime(29) = 107+109 =216 = 6^3.
%e A071220 n=1291597: prime(1291597)+prime(1291598) = 344*344*344.
%t A071220 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}]
%t A071220 Flatten[Position[Total/@Partition[Prime[Range[20000000]],2,1],_?(IntegerQ[ Surd[ #,3]]&)]] (* _Harvey P. Dale_, May 28 2014 *)
%o A071220 (Python)
%o A071220 from __future__ import division
%o A071220 from sympy import isprime, prevprime, nextprime, primepi
%o A071220 A071220_list, i = [], 2
%o A071220 while i < 10**6:
%o A071220     n = i**3
%o A071220     m = n//2
%o A071220     if not isprime(m) and prevprime(m) + nextprime(m) == n:
%o A071220         A071220_list.append(primepi(m))
%o A071220     i += 1 # _Chai Wah Wu_, May 31 2017
%Y A071220 Cf. A064397, A074925, A074924, A001043.
%K A071220 nonn
%O A071220 1,1
%A A071220 _Labos Elemer_, May 17 2002
%E A071220 Edited and extended by _Robert G. Wilson v_, Oct 07 2002