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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A034961, A127345.

Sequence in context: A127345 A127346 A089704 * A210548 A146353 A131633

Adjacent sequences: A287606 A287607 A287608 * A287610 A287611 A287612

Keyword

nonn

Author

Zak Seidov, May 27 2017

Extensions

More terms from Michael De Vlieger, May 28 2017

Status

approved