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A123984 Primes p such that p^3 is a sum of three successive primes, or primes in A076306(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A067355 A138362

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

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)