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A078855
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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, 4,2]; short d-string notation of pattern = [642].
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16
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31, 61, 271, 607, 1291, 1657, 1777, 1861, 1987, 2131, 2371, 2677, 2791, 4507, 5407, 5431, 5641, 7867, 9001, 11821, 13681, 14551, 17377, 18121, 18301, 20347, 21481, 22147, 24097, 27271, 32707, 35521, 36781, 37561, 41221, 41947, 42397, 42451
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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+4, p(i+3)=p+6+4+2.
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EXAMPLE
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p=31,31+6=37,31+6+4=41,31+6+4+2=43 are consecutive primes.
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MATHEMATICA
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Transpose[Select[Partition[Prime[Range[4500]], 4, 1], Differences[#] == {6, 4, 2}&]][[1]] (* Harvey P. Dale, Feb 10 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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