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A140250
a(n) is the largest cube <= A066525(n).
3
343, 15625, 34965783, 106496424, 3023464536, 3659383421, 7222633237, 10403062487, 11179320256, 11993263569, 25881801912, 36495256013, 40672093519, 47516597848, 49917330568, 63616767488, 84200449887, 96323848704, 573234910443, 972947676429
OFFSET
1,1
COMMENTS
Suggested by Carlos Rivera's Prime Puzzles & Problems Connection, Puzzle 443 (which asks if a sum of consecutive cubes can be a cube or a prime cube).
LINKS
Carlos Rivera, Puzzle 443. Sum of cubes of consecutive primes, The Prime Puzzles and Problems Connection.
EXAMPLE
In A066525 the first term is 503, the sum of cubes of the first four consecutive primes, 2 3 5 7. The cube just less than 503 is 343, a(1) in this sequence.
MAPLE
with(numtheory): P:=proc(n) add(ithprime(k)^3, k=1..n): end:
A098563 := proc(n)local m: option remember: if(n=0)then return 0: fi: m:=procname(n-1)+2: while true do if(isprime(P(m)))then return m:fi: m:=m+2:od: end:
A140250 := proc(n)return floor(surd(P(A098563(n)), 3))^3: end:
seq(A140250(n), n=1..20); # Nathaniel Johnston, Apr 21 2011
MATHEMATICA
Floor[CubeRoot[#]]^3&/@Select[Accumulate[Prime[Range[400]]^3], PrimeQ] (* Harvey P. Dale, May 22 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Enoch Haga, May 15 2008
EXTENSIONS
Edited by N. J. A. Sloane, Aug 25 2008
a(11)-a(20) from Nathaniel Johnston, Apr 21 2011
STATUS
approved