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Primes p with property that the sum of the cubes of the successive gaps between primes <= p is a prime number.
4

%I #24 May 01 2021 08:03:42

%S 7,13,31,103,157,211,229,277,283,337,349,367,373,379,433,463,499,523,

%T 547,577,613,619,643,673,751,907,937,1009,1021,1039,1123,1201,1231,

%U 1327,1399,1459,1489,1543,1579,1597,1669,1723,1777,1789,1831,1873,1933,1987,2011,2017

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

%H Abhiram R Devesh, <a href="/A247178/b247178.txt">Table of n, a(n) for n = 1..1000</a>

%e 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 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 (Python)

%o from sympy import nextprime, isprime

%o p=2

%o s=0

%o while 0 < p < 10000:

%o np=nextprime(p)

%o if isprime(s):

%o print(p)

%o d=np-p

%o s+=(d*d*d)

%o p=np

%K nonn,easy

%O 1,1

%A _Abhiram R Devesh_, Nov 22 2014