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

1,1

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

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.

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

Cf. A066525, A098563, A140251.

Sequence in context: A224427 A134263 A270820 * A117197 A269554 A046236

Adjacent sequences: A140247 A140248 A140249 * A140251 A140252 A140253

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