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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 (list; graph; refs; listen; history; text; internal format)
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: A047710 A063580 A003049 * A231398 A231465 A208820

Adjacent sequences:  A098560 A098561 A098562 * A098564 A098565 A098566

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Sep 14 2004

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)