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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.
1
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
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
KEYWORD
nonn,hard,more
AUTHOR
Abhiram R Devesh, Dec 21 2014
STATUS
approved