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

1,1

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

Formula

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

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 *)

Prog

(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

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.

Sequence in context: A219079 A059323 A267614 * A141282 A336181 A354590

Adjacent sequences: A123981 A123982 A123983 * A123985 A123986 A123987

Keyword

nonn

Author

Alexander Adamchuk, Oct 30 2006

Extensions

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

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

Status

approved