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A158796 Index of first of three successive primes which sum to a cube.

%I A158796 #12 Jun 01 2017 10:18:50
%S A158796 85,3696,79700,263166,283353,434935,678277,950264,1043678,1266169,
%T A158796 1321463,1436753,2629623,3568796,3604676,3676738,3713180,5096401,
%U A158796 5558697,7162624,9303565,9504536,10988577,12778681,13108392,18730119
%N A158796 Index of first of three successive primes which sum to a cube.
%H A158796 Chai Wah Wu, <a href="/A158796/b158796.txt">Table of n, a(n) for n = 1..1000</a>
%e A158796 a(1)=85 because prime(85)+prime(86)+prime(87)=439+443+449=11^3=(A076306(1))^3
%e A158796 a(2)=3696 because prime(3696)+prime(3697)+prime(3698)=34603+34607+34613=47^3=(A076306(2))^3.
%p A158796 count:= 0:
%p A158796 for x from 3 while count < 30 do
%p A158796   y:= x^3;
%p A158796   r:= floor(y/3);
%p A158796   p0:= prevprime(r); p1:= nextprime(p0); p2:= nextprime(p1);
%p A158796   while p0 + p1 + p2 > y do
%p A158796     p2:= p1;
%p A158796     p1:= p0;
%p A158796     p0:= prevprime(p0);
%p A158796   od:
%p A158796   while p0 + p1 + p2 < y do
%p A158796     p0:= p1;
%p A158796     p1:= p2;
%p A158796     p2:= nextprime(p2);
%p A158796   od:
%p A158796   if p0 + p1 + p2 = y then
%p A158796     count:= count+1;
%p A158796     A[count]:= numtheory:-pi(p0);
%p A158796   fi
%p A158796 od:
%p A158796 seq(A[i],i=1..count); # _Robert Israel_, Feb 10 2017
%o A158796 (Python)
%o A158796 from __future__ import division
%o A158796 from sympy import prevprime, nextprime, isprime, primepi
%o A158796 A158796_list, i = [], 3
%o A158796 while i < 10**6:
%o A158796     n = i**3
%o A158796     m = n//3
%o A158796     pm, nm = prevprime(m), nextprime(m)
%o A158796     k = n - pm - nm
%o A158796     if isprime(m):
%o A158796         if m == k:
%o A158796             A158796_list.append(primepi(pm))
%o A158796     else:
%o A158796         if nextprime(nm) == k:
%o A158796             A158796_list.append(primepi(pm))
%o A158796         elif prevprime(pm) == k:
%o A158796             A158796_list.append(primepi(pm)-1)
%o A158796     i += 1 # _Chai Wah Wu_, Jun 01 2017
%Y A158796 Cf. A076304, A076306.
%K A158796 nonn
%O A158796 1,1
%A A158796 _Zak Seidov_, Nov 12 2009