A287609 - OEIS

%I #13 May 31 2017 09:33:20

%S 31,71,311,551,1151,14831,45791,455471,2035271,6345239,7241615,

%T 8290031,8329991,9086231,9324351,10449575,11497199,15454151,16515815,

%U 18337271,20650811,22946591,27609311,33220079,40487471,44106191,45015791,49021199,53315519,54536519

%N Intersection of A034961 and A127345.

%C Surprisingly many terms are prime numbers: 31,71,311,1151,14831,455471.

%C Positions of a(n) in A127345: {1,2,4,5,7,19,30,76,142}.

%C Positions of a(n) in A034961: {4,8,26,41,75,660,1780,14009,54929}.

%C 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 Chai Wah Wu, <a href="/A287609/b287609.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 Intersection[Map[Total, #], Map[#1 #2 + #1 #3 + #2 #3 & @@ # &, #]] &@ Partition[Prime@ Range[10^6], 3, 1] (* _Michael De Vlieger_, May 28 2017 *)

%o (Python)

%o from __future__ import division

%o from sympy import isprime, prevprime, nextprime

%o A287609_list, p, q, r = [], 2, 3, 5

%o while r < 10**6:

%o     n = p*(q+r) + q*r

%o     m = n//3

%o     pm, nm = prevprime(m), nextprime(m)

%o     k = n - pm - nm

%o     if isprime(m):

%o         if m == k:

%o             A287609_list.append(n)

%o     else:

%o         if nextprime(nm) == k or prevprime(pm) == k:

%o             A287609_list.append(n)

%o     p, q, r = q, r, nextprime(r) # _Chai Wah Wu_, May 31 2017

%Y Cf. A034961, A127345.

%K nonn

%O 1,1

%A _Zak Seidov_, May 27 2017

%E More terms from _Michael De Vlieger_, May 28 2017