A140250 a(n) is the largest cube <= A066525(n).

343, 15625, 34965783, 106496424, 3023464536, 3659383421, 7222633237, 10403062487, 11179320256, 11993263569, 25881801912, 36495256013, 40672093519, 47516597848, 49917330568, 63616767488, 84200449887, 96323848704, 573234910443, 972947676429

Offset: 1

Author

Enoch Haga, May 15 2008

Keywords

• nonn

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).

Examples

			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.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..1000
• Carlos Rivera, Puzzle 443. Sum of cubes of consecutive primes, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A066525, A098563, A140251.

Programs

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 *)

Extensions

Edited by N. J. A. Sloane, Aug 25 2008

a(11)-a(20) from Nathaniel Johnston, Apr 21 2011