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A287609 Intersection of A034961 and A127345.

%I A287609 #13 May 31 2017 09:33:20
%S A287609 31,71,311,551,1151,14831,45791,455471,2035271,6345239,7241615,
%T A287609 8290031,8329991,9086231,9324351,10449575,11497199,15454151,16515815,
%U A287609 18337271,20650811,22946591,27609311,33220079,40487471,44106191,45015791,49021199,53315519,54536519
%N A287609 Intersection of A034961 and A127345.
%C A287609 Surprisingly many terms are prime numbers: 31,71,311,1151,14831,455471.
%C A287609 Positions of a(n) in A127345: {1,2,4,5,7,19,30,76,142}.
%C A287609 Positions of a(n) in A034961: {4,8,26,41,75,660,1780,14009,54929}.
%C A287609 Positions of primes in a(n): {1,2,3,5,6,8,21,22,25,32,37,39,40,45,49,50, 59,62,66,69,...}. - _Michael De Vlieger_, May 28 2017
%H A287609 Chai Wah Wu, <a href="/A287609/b287609.txt">Table of n, a(n) for n = 1..10000</a>
%e A287609 31 is in the sequence because it is both the total of three consecutive primes (7 + 11 + 13) and it is (2*3 + 2*5 + 3*5) = (6 + 10 + 15). - _Michael De Vlieger_, May 28 2017
%t A287609 Intersection[Map[Total, #], Map[#1 #2 + #1 #3 + #2 #3 & @@ # &, #]] &@ Partition[Prime@ Range[10^6], 3, 1] (* _Michael De Vlieger_, May 28 2017 *)
%o A287609 (Python)
%o A287609 from __future__ import division
%o A287609 from sympy import isprime, prevprime, nextprime
%o A287609 A287609_list, p, q, r = [], 2, 3, 5
%o A287609 while r < 10**6:
%o A287609     n = p*(q+r) + q*r
%o A287609     m = n//3
%o A287609     pm, nm = prevprime(m), nextprime(m)
%o A287609     k = n - pm - nm
%o A287609     if isprime(m):
%o A287609         if m == k:
%o A287609             A287609_list.append(n)
%o A287609     else:
%o A287609         if nextprime(nm) == k or prevprime(pm) == k:
%o A287609             A287609_list.append(n)
%o A287609     p, q, r = q, r, nextprime(r) # _Chai Wah Wu_, May 31 2017
%Y A287609 Cf. A034961, A127345.
%K A287609 nonn
%O A287609 1,1
%A A287609 _Zak Seidov_, May 27 2017
%E A287609 More terms from _Michael De Vlieger_, May 28 2017