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Search: id:A052350
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| 5, 17, 41, 617, 71, 311, 2267, 521, 1877, 461, 1721, 347, 1151, 1787, 3581, 2141, 6449, 1319, 21377, 1487, 12251, 4799, 881, 23057, 659, 19541, 12377, 2381, 38747, 10529, 37361, 8627, 9041, 33827, 5879, 80231, 15359, 45821, 36107, 14627, 37991
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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1. Smallest distance (A052380) and also smallest possible increment of twin-distances is 6.
2. Primes may occur between p+2 and p+6n.
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FORMULA
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The prime a(n) determines a prime quadruple: [p, p+2, p+6n, p+6n+2] and a [2, 6n-2, 2] d-pattern.
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EXAMPLE
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1. The first 3 terms (5,17,47) are followed by difference patterns as it is displayed: 5 by [2,4,2], 17 by [2,4+6,2], 41 by [2,4+6+6,2] determining prime quadruples: (5,7,11,13), (17,19,29,31) or (41,43,59,61) resp.
2. n=10 gives the quadruple [461,463,521=461+60,523] and between 521 and 463 7 primes occur.
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MATHEMATICA
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NextLowerTwinPrim[n_] := Block[{k = n + 6}, While[ !PrimeQ[k] || !PrimeQ[k + 2], k += 6]; k]; p = 5; t = Table[0, {50}]; Do[ q = NextLowerTwinPrim[p]; d = (q - p)/6; If[d < 51 && t[[d]] == 0, t[[d]] = p; Print[{d, p}]]; p = q, {n, 1500}]; t (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 28 2005)
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CROSSREFS
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Cf. A001359, A053319, A007530, A053280, A053281, A113274, A113275.
Sequence in context: A106973 A102264 A122035 this_sequence A096741 A111746 A088645
Adjacent sequences: A052347 A052348 A052349 this_sequence A052351 A052352 A052353
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 07 2000
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