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

1,1

Comments

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

Links

Table of n, a(n) for n=1..7.

Abhiram R Devesh, Python code to generate this sequence

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A318541 A076903 A192987 * A062367 A286257 A168418

Adjacent sequences: A252765 A252766 A252767 * A252769 A252770 A252771

Keyword

nonn,hard,more

Author

Abhiram R Devesh, Dec 21 2014

Status

approved