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 A076306 Numbers k such that k^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 Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..252 from Zak Seidov, terms 253..1000 from Donovan Johnson) EXAMPLE 11 is a term because 11^3 = 1331 = prime(85) + prime(86) + prime(87) = 439 + 443 + 449. 47 is a term 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]  (* 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 */ (Python) from __future__ import division from sympy import nextprime, prevprime, isprime A070306_list, i = [], 3 while i < 10**6:     n = i**3     m = n//3     pm, nm = prevprime(m), nextprime(m)     k = n - pm - nm     if isprime(m):         if m == k:             A070306_list.append(i)     else:         if nextprime(nm) == k or prevprime(pm) == k:             A070306_list.append(i)     i += 1 # Chai Wah Wu, May 30 2017 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 August 4 02:10 EDT 2020. Contains 336201 sequences. (Running on oeis4.)