A287686 Numbers that are sums of three consecutive primes (A034961) and also sums of squares of three consecutive primes (A133529).

83, 366819, 1055019, 1947411, 2740107, 3694179, 6627579, 8851251, 9430899, 20243811, 28391619, 37545291, 38242083, 49459179, 56550291, 88205211, 101931891, 103429491, 108060339, 135085851, 176962659, 183973851, 194907051, 196911171, 212874531, 249687699, 271986651

Offset: 1

Author

Zak Seidov, May 29 2017

Keywords

• nonn

Comments

The only prime number is 83.

Examples

			83=A034961(9)=A133529(2),
366819=A034961(11502)=A133529(69),
1055019=A034961(30105)=A133529(107),
1947411=A034961(52758)=A133529(139),
2740107=A034961(72260)=A133529(161),
3694179=A034961(95152)=A133529(185).
		

Links

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

Crossrefs

Cf. A034961 Sums of three consecutive primes. A133529 Sum of squares of three consecutive primes.

Programs

Python

from _future_ import division
from sympy import prevprime, nextprime, isprime
A287686_list, p2, q2, r2, r = [], 4, 9, 25, 5
while r < 10**6:
    n = p2+q2+r2
    m = n//3
    pm, nm = prevprime(m), nextprime(m)
    k = n - pm - nm
    if isprime(m):
        if m == k:
            A287686_list.append(n)
    else:
        if nextprime(nm) == k or prevprime(pm) == k:
            A287686_list.append(n)
    s = nextprime(r)
    p2, q2, r2, r = q2, r2, s**2, s # Chai Wah Wu, May 30 2017