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A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529).

%I A287686 #10 May 30 2017 23:29:15
%S A287686 83,366819,1055019,1947411,2740107,3694179,6627579,8851251,9430899,
%T A287686 20243811,28391619,37545291,38242083,49459179,56550291,88205211,
%U A287686 101931891,103429491,108060339,135085851,176962659,183973851,194907051,196911171,212874531,249687699,271986651
%N A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529).
%C A287686 The only prime number is 83.
%H A287686 Chai Wah Wu, <a href="/A287686/b287686.txt">Table of n, a(n) for n = 1..10000</a>
%e A287686 83=A034961(9)=A133529(2),
%e A287686 366819=A034961(11502)=A133529(69),
%e A287686 1055019=A034961(30105)=A133529(107),
%e A287686 1947411=A034961(52758)=A133529(139),
%e A287686 2740107=A034961(72260)=A133529(161),
%e A287686 3694179=A034961(95152)=A133529(185).
%o A287686 (Python)
%o A287686 from __future__ import division
%o A287686 from sympy import prevprime, nextprime, isprime
%o A287686 A287686_list, p2, q2, r2, r = [], 4, 9, 25, 5
%o A287686 while r < 10**6:
%o A287686     n = p2+q2+r2
%o A287686     m = n//3
%o A287686     pm, nm = prevprime(m), nextprime(m)
%o A287686     k = n - pm - nm
%o A287686     if isprime(m):
%o A287686         if m == k:
%o A287686             A287686_list.append(n)
%o A287686     else:
%o A287686         if nextprime(nm) == k or prevprime(pm) == k:
%o A287686             A287686_list.append(n)
%o A287686     s = nextprime(r)
%o A287686     p2, q2, r2, r = q2, r2, s**2, s # _Chai Wah Wu_, May 30 2017
%Y A287686 Cf. A034961 Sums of three consecutive primes. A133529 Sum of squares of three consecutive primes.
%K A287686 nonn
%O A287686 1,1
%A A287686 _Zak Seidov_, May 29 2017