A123984 Primes p such that p^3 is a sum of three successive primes, or primes in A076306(n).

11, 47, 223, 229, 313, 353, 397, 409, 571, 641, 661, 887, 1051, 1297, 1451, 1789, 2459, 2671, 2801, 2851, 3671, 4463, 4583, 4813, 4861, 5167, 5273, 5437, 5479, 5717, 5879, 6661, 6679, 6763, 6779, 7019, 7109, 7393, 7517, 7589, 7639, 7681, 7993, 8179, 8191, 9241

Offset: 1

Author

Alexander Adamchuk, Oct 30 2006

Keywords

• nonn

Comments

A076306(n) = {11, 47, 145, 223, 229, 267, 313, 353, ...} Numbers n such that n^3 is a sum of three successive primes.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000

Crossrefs

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.

Programs

Mathematica

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 *)

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

Formula

A000040 INTERSECT A076306. - R. J. Mathar, Jan 13 2007

Extensions

More terms from R. J. Mathar, Jan 13 2007

a(15)-a(46) from Donovan Johnson, Apr 27 2008