A226524 Cubes which are the sum of two consecutive primes.

8, 216, 21952, 74088, 373248, 4251528, 5268024, 10648000, 10941048, 12812904, 14886936, 16003008, 25934336, 40707584, 54872000, 59319000, 114791256, 132651000, 199176704, 209584584, 259694072, 269586136, 306182024, 345948408, 373248000, 543338496, 567663552

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Donovan Johnson)

Formula

a(n) = A074925(n)^3 = A000040(i) + A000040(i+1) with i = A071220(n) = A000720(A061308(n)). - M. F. Hasler, Jan 03 2020

Example

a(2) = 216: prime(28) + prime(29) = 107 + 109 = 216 = 6^3.

Maple

KD: = proc() local a, b, c;  a: = ithprime(n) + ithprime(n+1); b:= evalf(a^(1/3)); if b=floor(b) then RETURN(a):  fi; end: seq(KD(), n=1..1000000);

Mathematica

Select[Total/@Partition[Prime[Range[155*10^5]], 2, 1], IntegerQ[Surd[#, 3]]&] (* or *) stcpQ[n_]:=Module[{p1=NextPrime[Floor[n/2], -1], p2=NextPrime[Ceiling[n/2]]}, n==p1+p2]; Select[Range[850]^3, stcpQ] (* The second program is much more efficient than the first. *) (* Harvey P. Dale, May 15 2022 *)

Prog

(PARI) n=0; forstep(j=2, 55778, 2, c=j^3; c2=c/2; if(precprime(c2)+nextprime(c2)==c, n++; write("b226524.txt", n " " c))) /* Donovan Johnson, Sep 02 2013 */
(PARI) A226524(n)=A074925(n)^3 \\ M. F. Hasler, Jan 03 2020
(Python)
from itertools import count, islice
from sympy import nextprime, prevprime
def agen(): yield from (c for c in (k**3 for k in count(2, step=2)) if prevprime(c//2+1) + nextprime(c//2-1) == c)
print(list(islice(agen(), 27))) # Michael S. Branicky, May 24 2022

Crossrefs

Cubes in A001043.

Cf. A062703 (analog for squares), A061308 (lesser of the consecutive primes), A071220 (index of that prime), A074925 (a(n)^(1/3)).

Sequence in context: A000442 A268471 A342598 * A359412 A115964 A245591

Adjacent sequences: A226521 A226522 A226523 * A226525 A226526 A226527

Keyword

nonn,easy

Author

K. D. Bajpai, Aug 31 2013

Extensions

Edited by M. F. Hasler, Jan 03 2020

Status

approved