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A078854
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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 d-pattern=[6, 2,6]; short d-string notation of pattern = [626].
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17
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23, 53, 263, 563, 593, 1223, 1283, 1613, 2333, 2543, 3533, 4013, 4643, 5843, 6263, 6353, 6563, 10853, 11483, 14543, 15263, 17483, 19073, 19373, 19463, 23663, 26723, 29123, 32363, 34253, 41603, 48473, 49193, 49523, 51413, 51473, 71333, 75983
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Primes p = p(i) such that p(i+1)=p+6, p(i+2)=p+6+2, p(i+3)=p+6+2+6.
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EXAMPLE
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p=23,23+6=29,23+6+2=31,23+6+2+6=37 are consecutive primes.
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MATHEMATICA
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Transpose[Select[Partition[Prime[Range[7500]], 4, 1], Differences[#]=={6, 2, 6}&]][[1]] (* Harvey P. Dale, Apr 17 2015 *)
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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].
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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