A076306 Numbers k such that k^3 is a sum of three successive primes.
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
Offset: 1
Keywords
Examples
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.
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)
Programs
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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 *) -
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
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
Comments