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%I #21 Aug 23 2022 08:45:08
%S 17,134764997,9844128377,345828727877,9637575539147,223528482767957,
%T 4652382265065167,89306626080020957
%N a(n) = A022012(10^n).
%C The terms are the (10^n)-th initial members of the prime octuplets of the form (p, p+2, p+6, p+12, p+14, p+20, p+24, 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).
%C Asymptotically for n -> infinity, C_HL*Integral_{x=2..a(n)} 1/log(x)^8 dx = 10^n, where C_HL = 475.36521172411318772... is the specific Hardy-Littlewood constant for this prime constellation. The predicted approximate values using this relationship would be a(6) = 4.629899*10^15 and a(7) = 8.9223552*10^16.
%H Norman Luhn, <a href="https://pzktupel.de/counting/PI_08.php">Number of 8-tuplets with initial members < 10^n</a>, (2021).
%Y Cf. A022011, A022012, A022013, A210439, A332493, A346996, A346998.
%K nonn,hard,more
%O 0,1
%A _Hugo Pfoertner_, Aug 11 2021
%E a(7) from _Norman Luhn_, Sep 13 2021
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