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%I #12 Aug 22 2015 09:44:35
%S 4,8,38,48,98,102,118,128,130,132,156,168,172,178,180,190,202,208,308,
%T 346,358,364,424,482,540,600,602,614,646,676,722,748,768,776,782,792,
%U 838,902,1016,1028,1036,1058,1062,1082,1086,1100,1102,1132,1144,1176
%N Numbers n such that the sum of the cubes of the first n primes is prime.
%C n must clearly be even.
%H Nathaniel Johnston, <a href="/A098563/b098563.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%p with(numtheory): P:=proc(n) add(ithprime(k)^3, k=1..n): end:
%p 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:
%p seq(A098563(n), n=1..50); # _Nathaniel Johnston_, Apr 21 2011
%t Select[Range[1000], PrimeQ[Sum[Prime[i]^3, {i, #}]] &] (* _Carl Najafi_, Aug 22 2011 *)
%o (PARI) lista(nn) = {s = 0; ip = 0; forprime (p=1, nn, ip++; if (isprime(s+=p^3), print1(ip, ", ")););} \\ _Michel Marcus_, Aug 22 2015
%Y Cf. A066525 (corresponding primes), A098561 (sums of squares of primes), A013916 (sums of primes), A098999 (sums of cubes of primes).
%K nonn
%O 1,1
%A _Rick L. Shepherd_, Sep 14 2004
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