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A252768
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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.
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1
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OFFSET
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1,1
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COMMENTS
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This is a subsequence of A006512 (greater of twin primes), see comment by Robert G. Wilson v there. - Michel Marcus, Jan 23 2015
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LINKS
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Table of n, a(n) for n=1..7.
Abhiram R Devesh, Python code to generate this sequence
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A006512, A247177, A247178, A251623, A252655.
Sequence in context: A318541 A076903 A192987 * A062367 A286257 A168418
Adjacent sequences: A252765 A252766 A252767 * A252769 A252770 A252771
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KEYWORD
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nonn,hard,more
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AUTHOR
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Abhiram R Devesh, Dec 21 2014
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STATUS
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approved
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