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OFFSET
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0,1
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COMMENTS
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The terms are the (10^n)-th initial members of the prime octuplets of the form (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26). Terms a(5) and a(6) were found using a program provided by Norman Luhn during an effort to find A210439(8) and A332493(8).
Asymptotically for n -> infinity, C_HL*Integral_{x=2..a(n)} 1/log(x)^8 dx = 10^n, where C_HL = 178.261954396542445395360788... is the specific Hardy-Littlewood constant for this prime constellation. The predicted approximate values using this relationship would be a(6) = 1.647755*10^16 and a(7) = 3.0824636*10^17.
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LINKS
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Table of n, a(n) for n=0..7.
Norman Luhn, Number of 8-tuplets with initial members < 10^n, (2021).
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CROSSREFS
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Cf. A022011, A022012, A022013, A210439, A332493, A346997, A346998.
Sequence in context: A347849 A295173 A022545 * A086503 A275573 A247846
Adjacent sequences: A346993 A346994 A346995 * A346997 A346998 A346999
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KEYWORD
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nonn,hard,more
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AUTHOR
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Hugo Pfoertner, Aug 11 2021
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EXTENSIONS
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a(7) from Norman Luhn and Hugo Pfoertner, Sep 14 2021
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STATUS
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approved
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