A252768 Primes p with property that the sum of the k-th powers of the successive gaps between primes <= p are prime numbers for k = 1 to n.

5, 5, 13, 14593, 372313, 2315773, 541613713

Offset: 1

Author

Abhiram R Devesh, Dec 21 2014

Keywords

• nonn
• hard
• more

Comments

This is a subsequence of A006512 (greater of twin primes), see comment by Robert G. Wilson v there. - Michel Marcus, Jan 23 2015

Examples

			n=3, p=13, List of primes [2, 3, 5, 7, 11, 13] and respective prime gaps are [1, 2, 2, 4, 2].
k=1: Sum of prime gaps = 11.
k=2: Sum of squares of prime gaps = 29.
k=3: Sum of cubes of prime gaps = 89.
		

Links

• Abhiram R Devesh, Python code to generate this sequence

Crossrefs

Cf. A006512, A247177, A247178, A251623, A252655.

Programs

PARI

a(n) = {vp = primes(200000); vdp = vector(#vp-1, k, vp[k+1] - vp[k]); vpp = vector(n, k, 1); k = 2; while (sum(m=1, n, isprime(vpp[m])) != n, for (j=1, n, vpp[j] += vdp[k]^j;); k++;); vp[k];} \\ Michel Marcus, Jan 23 2015