A098563 Numbers n such that the sum of the cubes of the first n primes is prime.

4, 8, 38, 48, 98, 102, 118, 128, 130, 132, 156, 168, 172, 178, 180, 190, 202, 208, 308, 346, 358, 364, 424, 482, 540, 600, 602, 614, 646, 676, 722, 748, 768, 776, 782, 792, 838, 902, 1016, 1028, 1036, 1058, 1062, 1082, 1086, 1100, 1102, 1132, 1144, 1176

Offset

1,1

Comments

n must clearly be even.

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

Example

4 is a term as the sum of the cubes of the first four primes is 2^3 + 3^3 + 5^3 + 7^3 = 503, which is prime.

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:
seq(A098563(n), n=1..50); # Nathaniel Johnston, Apr 21 2011

Mathematica

Select[Range[1000], PrimeQ[Sum[Prime[i]^3, {i, #}]] &] (* Carl Najafi, Aug 22 2011 *)

Prog

(PARI) lista(nn) = {s = 0; ip = 0; forprime (p=1, nn, ip++; if (isprime(s+=p^3), print1(ip, ", ")); ); } \\ Michel Marcus, Aug 22 2015

Crossrefs

Cf. A066525 (corresponding primes), A098561 (sums of squares of primes), A013916 (sums of primes), A098999 (sums of cubes of primes).

Sequence in context: A335991 A063580 A003049 * A231398 A231465 A208820

Adjacent sequences: A098560 A098561 A098562 * A098564 A098565 A098566

Keyword

nonn

Author

Rick L. Shepherd, Sep 14 2004

Status

approved