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A078847
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Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <= 6 (i.e., when d = 2, 4 or 6) and forming pattern = [2, 4, 6]; short notation = [246] d-pattern.
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28
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17, 41, 227, 347, 641, 1091, 1277, 1427, 1487, 1607, 2687, 3527, 3917, 4001, 4127, 4637, 4787, 4931, 8231, 9461, 10331, 11777, 12107, 13901, 14627, 20747, 21557, 23741, 25577, 26681, 26711, 27737, 27941, 28277, 29021, 31247, 32057, 32297
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OFFSET
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1,1
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COMMENTS
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Subsequence of A022004. - R. J. Mathar, Feb 10 2013
a(n) + 12 is the greatest term in the sequence of 4 consecutive primes with 3 consecutive gaps 2, 4, 6. - Muniru A Asiru, Aug 03 2017
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..2000
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FORMULA
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Primes p=prime(i) such that prime(i+1) = p+2, prime(i+2) = p+2+4, prime(i+3) = p+2+4+6.
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EXAMPLE
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17, 17+2 = 19, 17+2+4 = 23, 17+2+4+6 = 29 are consecutive primes.
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MATHEMATICA
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d = Differences[Prime[Range[10000]]]; Prime[Flatten[Position[Partition[d, 3, 1], {2, 4, 6}]]] (* T. D. Noe, May 23 2011 *)
Transpose[Select[Partition[Prime[Range[10000]], 4, 1], Differences[#] == {2, 4, 6}&]][[1]] (* Harvey P. Dale, Aug 07 2013 *)
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CROSSREFS
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Cf. analogous prime quadruple sequences with various possible {2, 4, 6}-difference-patterns in brackets: A007530[242], A078847[246], A078848[264], A078849[266], A052378[424], A078850[426], A078851[462], A078852[466], A078853[624], A078854[626], A078855[642], A078856[646], A078857[662], A078858[664], A033451[666].
Cf. A190814[2,4,6,8], A190817[2,4,6,8,10], A190819[2,4,6,8,10,12], A190838[2,4,6,8,10,12,14]
Sequence in context: A165668 A269425 A164602 * A201028 A328022 A287308
Adjacent sequences: A078844 A078845 A078846 * A078848 A078849 A078850
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Dec 11 2002
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EXTENSIONS
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Listed terms verified by Ray Chandler, Apr 20 2009
Additional cross references from Harvey P. Dale, May 10 2014
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STATUS
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approved
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