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A098563
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Numbers n such that the sum of the cubes of the first n primes is prime.
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4
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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; internal format)
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OFFSET
| 1,1
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COMMENTS
| n must clearly be even.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..1000
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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.
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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
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MATHEMATICA
| Select[Range[1000], PrimeQ[Sum[Prime[i]^3, {i, #}]] &] (* Carl Najafi, Aug 22 2011 *)
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CROSSREFS
| Cf. A066525 (corresponding primes), A098561 (sums of squares of primes), A013916 (sums of primes).
Sequence in context: A047710 A063580 A003049 * A032301 A032213 A032317
Adjacent sequences: A098560 A098561 A098562 * A098564 A098565 A098566
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Sep 14 2004
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