A287609 Intersection of A034961 and A127345.

31, 71, 311, 551, 1151, 14831, 45791, 455471, 2035271, 6345239, 7241615, 8290031, 8329991, 9086231, 9324351, 10449575, 11497199, 15454151, 16515815, 18337271, 20650811, 22946591, 27609311, 33220079, 40487471, 44106191, 45015791, 49021199, 53315519, 54536519

Offset: 1

Author

Zak Seidov, May 27 2017

Keywords

• nonn

Comments

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

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

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

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

Examples

			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
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A034961, A127345.

Programs

Mathematica

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

Python

from _future_ import division
from sympy import isprime, prevprime, nextprime
A287609_list, p, q, r = [], 2, 3, 5
while r < 10**6:
    n = p*(q+r) + q*r
    m = n//3
    pm, nm = prevprime(m), nextprime(m)
    k = n - pm - nm
    if isprime(m):
        if m == k:
            A287609_list.append(n)
    else:
        if nextprime(nm) == k or prevprime(pm) == k:
            A287609_list.append(n)
    p, q, r = q, r, nextprime(r) # Chai Wah Wu, May 31 2017

Extensions

More terms from Michael De Vlieger, May 28 2017