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

1,1

Links

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

Example

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.

Prog

(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

Crossrefs

Sequence in context: A239679 A195353 A342184 * A053183 A247955 A026318

Adjacent sequences: A247175 A247176 A247177 * A247179 A247180 A247181

Keyword

nonn,easy

Author

Abhiram R Devesh, Nov 22 2014

Status

approved