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A076306 Numbers n such that n^3 is a sum of three successive primes. 4
11, 47, 145, 223, 229, 267, 313, 353, 365, 391, 397, 409, 507, 565, 567, 571, 573, 641, 661, 723, 793, 799, 841, 887, 895, 1015, 1051, 1089, 1293, 1297, 1411, 1451, 1469, 1789, 1909, 1943, 2043, 2077, 2171, 2401, 2459, 2497, 2671, 2801, 2851, 2871, 2921, 3211 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

prime(k) + prime(k+1) + prime(k+2) is a cube in A034961, k=A158796(n).

LINKS

Zak Seidov and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 252 terms from Zak Seidov)

EXAMPLE

11 is OK because 11^3 = 1331 = prime(85)+prime(86)+prime(87) = 439+443+449.

47 is OK because 47^3 = 103823 = prime(3696)+prime(3697)+prime(3698) = 34603+34607+34613.

MATHEMATICA

okQ[n_]:=Module[{x=n^3, low, hi}, low=PrimePi[Round[x/3]]-4; hi=low+8; MemberQ[Total/@Partition[Prime[Range[low, hi]], 3, 1], x]]; Select[Range[5, 3300], okQ]  [From Harvey P. Dale, Jan 27 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), print(n) ; ) ; n3 -= p1 ; p1=p2 ; p2=p3 ; p3=nextprime(p3+1) ; n3 += p3 ; ) ; } - R. J. Mathar, Jan 13 2007

(PARI) n=0; forstep(j=3, 86231, 2, c=j^3; c3=c/3; f=0; if(denominator(c3)==1, if(isprime(c3), if(precprime(c3-1)+c3+nextprime(c3+1)==c, f=1))); p2=precprime(c3); p1=precprime(p2-1); p3=nextprime(c3); p4=nextprime(p3+1); if(p1+p2+p3==c, f=1); if(p2+p3+p4==c, f=1); if(f==1, n++; write("b076306.txt", n " " j))) /* Donovan Johnson, Sep 02 2013 */

CROSSREFS

Cf. A076304, A076305, A034961, A158796, A227475.

Sequence in context: A143830 A178572 A036489 * A219079 A059323 A267614

Adjacent sequences:  A076303 A076304 A076305 * A076307 A076308 A076309

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 05 2002, Nov 12 2009

EXTENSIONS

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

a(29)-a(48) from Donovan Johnson, Apr 27 2008

Edited by N. J. A. Sloane, Nov 12 2009 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified March 27 16:36 EDT 2017. Contains 284177 sequences.