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Square pyramidal numbers which are sums of three consecutive primes.
1

%I #7 Dec 31 2015 11:32:19

%S 1015,25585,1623245,2127685,7838831,8865649,19849115,52051769,

%T 73998155,88409285,91753025,161553785,216862421,289872105,347016319,

%U 382029011,466430159,835713879,1077314939,1223359835,1509659555,1584781241

%N Square pyramidal numbers which are sums of three consecutive primes.

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

%H Chai Wah Wu, <a href="/A167807/b167807.txt">Table of n, a(n) for n = 1..10000</a>

%e 1015=A034961(67)=A000330(14)

%e 25585=A034961(1062)=A000330(42).

%o (Python)

%o from __future__ import division

%o from sympy import nextprime, prevprime

%o A167807_list = []

%o for i in range(3,10**6):

%o n = i*(i+1)*(2*i+1)//6

%o p2 = prevprime(n//3)

%o p1, p3 = prevprime(p2), nextprime(p2)

%o q = p1+p2+p3

%o while q <= n:

%o if q == n:

%o A167807_list.append(n)

%o p1, p2, p3 = p2, p3, nextprime(p3)

%o q = p1+p2+p3 # _Chai Wah Wu_, Dec 31 2015

%Y Cf. A000330, A034961.

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 12 2009

%E a(6)-a(22) from _Donovan Johnson_, Nov 15 2009