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%I #21 May 28 2018 10:41:17
%S 11,47,223,229,313,353,397,409,571,641,661,887,1051,1297,1451,1789,
%T 2459,2671,2801,2851,3671,4463,4583,4813,4861,5167,5273,5437,5479,
%U 5717,5879,6661,6679,6763,6779,7019,7109,7393,7517,7589,7639,7681,7993,8179,8191,9241
%N Primes p such that p^3 is a sum of three successive primes, or primes in A076306(n).
%C A076306(n) = {11, 47, 145, 223, 229, 267, 313, 353, ...} Numbers n such that n^3 is a sum of three successive primes.
%H Donovan Johnson, <a href="/A123984/b123984.txt">Table of n, a(n) for n = 1..1000</a>
%F A000040 INTERSECT A076306. - _R. J. Mathar_, Jan 13 2007
%t spQ[n_]:=Module[{n3=n^3,a,b,c,d,e},c=NextPrime[Floor[n3/3]];b=NextPrime[ c,-1];a=NextPrime[b,-1];d=NextPrime[c];e=NextPrime[d];n3==a+b+c || n3==b+c+d || n3==c+d+e];Select[Prime[Range[1200]],spQ] (* _Harvey P. Dale_, Sep 23 2011 *)
%o (PARI) { p1=prime(1) ; p2=prime(2) ; p3=prime(3) ; n3=p1+p2+p3 ; for(i=1,100000000, if( ispower(n3,3,&n), if(isprime(n), print(n) ) ; ) ; n3 -= p1 ; p1=p2 ; p2=p3 ; p3=nextprime(p3+1) ; n3 += p3 ; ) ; } \\ _R. J. Mathar_, Jan 13 2007
%Y Cf. A076306, A076304. Cf. A122560 - Primes p such that p^2 is a sum of three successive primes. Cf. A122706 - Smallest prime p such that p^n is equal to the sum of 3 consecutive primes.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Oct 30 2006
%E More terms from _R. J. Mathar_, Jan 13 2007
%E a(15)-a(46) from _Donovan Johnson_, Apr 27 2008
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