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

%I A247178 #24 May 01 2021 08:03:42
%S A247178 7,13,31,103,157,211,229,277,283,337,349,367,373,379,433,463,499,523,
%T A247178 547,577,613,619,643,673,751,907,937,1009,1021,1039,1123,1201,1231,
%U A247178 1327,1399,1459,1489,1543,1579,1597,1669,1723,1777,1789,1831,1873,1933,1987,2011,2017
%N A247178 Primes p with property that the sum of the cubes of the successive gaps between primes <= p is a prime number.
%H A247178 Abhiram R Devesh, <a href="/A247178/b247178.txt">Table of n, a(n) for n = 1..1000</a>
%e A247178 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.
%e A247178 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.
%o A247178 (Python)
%o A247178 from sympy import nextprime, isprime
%o A247178 p=2
%o A247178 s=0
%o A247178 while 0 < p < 10000:
%o A247178     np=nextprime(p)
%o A247178     if isprime(s):
%o A247178         print(p)
%o A247178     d=np-p
%o A247178     s+=(d*d*d)
%o A247178     p=np
%K A247178 nonn,easy
%O A247178 1,1
%A A247178 _Abhiram R Devesh_, Nov 22 2014