A167807 Square pyramidal numbers which are sums of three consecutive primes.

1015, 25585, 1623245, 2127685, 7838831, 8865649, 19849115, 52051769, 73998155, 88409285, 91753025, 161553785, 216862421, 289872105, 347016319, 382029011, 466430159, 835713879, 1077314939, 1223359835, 1509659555, 1584781241

Offset: 1

Author

Zak Seidov, Nov 12 2009

Keywords

• nonn

Comments

Intersection of A000330 (Square pyramidal numbers) and A034961 (Sums of three consecutive primes).

Examples

			1015=A034961(67)=A000330(14)
25585=A034961(1062)=A000330(42).
		

Links

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

Crossrefs

Cf. A000330, A034961.

Programs

Python

from _future_ import division
from sympy import nextprime, prevprime
A167807_list = []
for i in range(3,10**6):
    n = i*(i+1)*(2*i+1)//6
    p2 = prevprime(n//3)
    p1, p3 = prevprime(p2), nextprime(p2)
    q = p1+p2+p3
    while q <= n:
        if q == n:
            A167807_list.append(n)
        p1, p2, p3 = p2, p3, nextprime(p3)
        q = p1+p2+p3 # Chai Wah Wu, Dec 31 2015

Extensions

a(6)-a(22) from Donovan Johnson, Nov 15 2009