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A226502
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Let P(k) denote the k-th prime (P(1)=2, P(2)=3 ...); a(n) = P(n+1)P(n+3) - P(n)P(n+2).
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2
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11, 34, 36, 96, 60, 144, 160, 162, 360, 198, 320, 336, 352, 494, 460, 720, 378, 560, 718, 450, 972, 1020, 938, 1002, 816, 420, 864, 1752, 960, 2596, 810, 2204, 576, 2404, 1220, 1606, 1980, 1694, 1420, 2876, 744, 2694, 780, 3160, 2810, 3520, 3170, 1824, 1840, 1422, 3836
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OFFSET
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1,1
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COMMENTS
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Differences of the products of alternate primes.
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LINKS
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FORMULA
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a(n) >> n log n and this is probably sharp: on Dickson's conjecture there are infinitely many a(n) < kn log n for any k > 4. The constant 4 comes from 8 + 2 - 6 - 0 n the prime quadruplet (p+0, p+2, p+6, p+8). On Cramér's conjecture a(n) = O(n log^3 n). Unconditionally a(n) << n^1.525 log n. - Charles R Greathouse IV, Jun 10 2013
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PROG
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(PARI) p=2; q=3; r=5; forprime(s=7, 1e2, print1(q*s-p*r", "); p=q; q=r; r=s) \\ Charles R Greathouse IV, Jun 10 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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