A247178 Primes p with property that the sum of the cubes of the successive gaps between primes <= p is a prime number.

7, 13, 31, 103, 157, 211, 229, 277, 283, 337, 349, 367, 373, 379, 433, 463, 499, 523, 547, 577, 613, 619, 643, 673, 751, 907, 937, 1009, 1021, 1039, 1123, 1201, 1231, 1327, 1399, 1459, 1489, 1543, 1579, 1597, 1669, 1723, 1777, 1789, 1831, 1873, 1933, 1987, 2011, 2017

Offset: 1

Author

Abhiram R Devesh, Nov 22 2014

Keywords

• nonn
• easy

Examples

			a(1)=7; primes less than or equal to 7: [2, 3, 5, 7]; cubes of prime gaps: [1, 8, 8]; sum of squares of prime gaps: 17.
a(2)=13; primes less than or equal to 13: [2, 3, 5, 7, 11, 13]; cubes of prime gaps: [1, 8, 8, 64, 8]; sum of squares of prime gaps: 89.
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..1000

Programs

Python

from sympy import nextprime, isprime
p=2
s=0
while 0 < p < 10000:
    np=nextprime(p)
    if isprime(s):
        print(p)
    d=np-p
    s+=(d*d*d)
    p=np