login
A098563
Numbers n such that the sum of the cubes of the first n primes is prime.
4
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
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 14 2004
STATUS
approved