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 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 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

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Last modified January 21 13:55 EST 2020. Contains 331113 sequences. (Running on oeis4.)